Precoding method, precoding device

ABSTRACT

Disclosed is a precoding method for generating, from a plurality of baseband signals, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time. According to the precoding method, one matrix is selected from among matrices defining a precoding process that is performed on the plurality of baseband signals by hopping between the matrices. A first baseband signal and a second baseband signal relating to a first coded block and a second coded block generated by using a predetermined error correction block coding scheme satisfy a given condition.

TECHNICAL FIELD

This application is based on Japanese Patent Application No. 2011-035086filed (on Feb. 21, 2011) in Japan, the contents of which are herebyincorporated by reference.

The present invention relates to a precoding scheme, a precoding device,a transmission scheme, a transmission device, a reception scheme, and areception device that in particular perform communication using amulti-antenna.

BACKGROUND ART

Multiple-Input Multiple-Output (MIMO) is a conventional example of acommunication scheme using a multi-antenna. In multi-antennacommunication, of which MIMO is representative, multiple transmissionsignals are each modulated, and each modulated signal is transmittedfrom a different antenna simultaneously in order to increase thetransmission speed of data.

FIG. 28 shows an example of the structure of a transmission andreception device when the number of transmit antennas is two, the numberof receive antennas is two, and the number of modulated signals fortransmission (transmission streams) is two. In the transmission device,encoded data is interleaved, the interleaved data is modulated, andfrequency conversion and the like is performed to generate transmissionsignals, and the transmission signals are transmitted from antennas. Inthis case, the scheme for simultaneously transmitting differentmodulated signals from different transmit antennas at the same time andat the same frequency is a spatial multiplexing MIMO system.

In this context, it has been suggested in Patent Literature 1 to use atransmission device provided with a different interleave pattern foreach transmit antenna. In other words, the transmission device in FIG.28 would have two different interleave patterns with respectiveinterleaves (πa, πb). As shown in Non-Patent Literature 1 and Non-PatentLiterature 2, reception quality is improved in the reception device byiterative performance of a detection scheme that uses soft values (theMIMO detector in FIG. 28).

Models of actual propagation environments in wireless communicationsinclude non-line of sight (NLOS), of which a Rayleigh fading environmentis representative, and line of sight (LOS), of which a Rician fadingenvironment is representative. When the transmission device transmits asingle modulated signal, and the reception device performs maximal ratiocombining on the signals received by a plurality of antennas and thendemodulates and decodes the signal resulting from maximal ratiocombining, excellent reception quality can be achieved in an LOSenvironment, in particular in an environment where the Rician factor islarge, which indicates the ratio of the received power of direct wavesversus the received power of scattered waves. However, depending on thetransmission system (for example, spatial multiplexing MIMO system), aproblem occurs in that the reception quality deteriorates as the Ricianfactor increases (see Non-Patent Literature 3).

FIGS. 29A and 29B show an example of simulation results of the Bit ErrorRate (BER) characteristics (vertical axis: BER, horizontal axis:signal-to-noise power ratio (SNR)) for data encoded with low-densityparity-check (LDPC) code and transmitted over a 2×2 (two transmitantennas, two receive antennas) spatial multiplexing MIMO system in aRayleigh fading environment and in a Rician fading environment withRician factors of K=3, 10, and 16 dB. FIG. 29A shows the BERcharacteristics of Max-log A Posteriori Probability (APP) withoutiterative detection (see Non-Patent Literature 1 and Non-PatentLiterature 2), and FIG. 29B shows the BER characteristics of Max-log-APPwith iterative detection (see Non-Patent Literature 1 and Non-PatentLiterature 2) (number of iterations: five). As is clear from FIGS. 29Aand 29B, regardless of whether iterative detection is performed,reception quality degrades in the spatial multiplexing MIMO system asthe Rician factor increases. It is thus clear that the unique problem of“degradation of reception quality upon stabilization of the propagationenvironment in the spatial multiplexing MIMO system”, which does notexist in a conventional single modulation signal transmission system,occurs in the spatial multiplexing MIMO system.

Broadcast or multicast communication is a service directed towardsline-of-sight users. The radio wave propagation environment between thebroadcasting station and the reception devices belonging to the users isoften an LOS environment. When using a spatial multiplexing MIMO systemhaving the above problem for broadcast or multicast communication, asituation may occur in which the received electric field strength ishigh at the reception device, but degradation in reception quality makesit impossible to receive the service. In other words, in order to use aspatial multiplexing MIMO system in broadcast or multicast communicationin both an NLOS environment and an LOS environment, there is a desirefor development of a MIMO system that offers a certain degree ofreception quality.

Non-Patent Literature 8 describes a scheme to select a codebook used inprecoding (i.e. a precoding matrix, also referred to as a precodingweight matrix) based on feedback information from a communicationpartner. Non-Patent Literature 8 does not at all disclose, however, ascheme for precoding in an environment in which feedback informationcannot be acquired from the communication partner, such as in the abovebroadcast or multicast communication.

On the other hand, Non-Patent Literature 4 discloses a scheme forhopping the precoding matrix over time. This scheme can be applied evenwhen no feedback information is available. Non-Patent Literature 4discloses using a unitary matrix as the matrix for precoding and hoppingthe unitary matrix at random but does not at all disclose a schemeapplicable to degradation of reception quality in the above-describedLOS environment. Non-Patent Literature 4 simply recites hopping betweenprecoding matrices at random. Obviously, Non-Patent Literature 4 makesno mention whatsoever of a precoding scheme, or a structure of aprecoding matrix, for remedying degradation of reception quality in anLOS environment.

CITATION LIST Patent Literature

-   Patent Literature 1: WO 2005/050885

Non-Patent Literature

-   Non-Patent Literature 1: “Achieving near-capacity on a    multiple-antenna channel”, IEEE Transaction on Communications, vol.    51, no. 3, pp. 389-399, March 2003.-   Non-Patent Literature 2: “Performance analysis and design    optimization of LDPC-coded MIMO OFDM systems”, IEEE Trans. Signal    Processing, vol. 52, no. 2, pp. 348-361, February 2004.-   Non-Patent Literature 3: “BER performance evaluation in 2×2 MIMO    spatial multiplexing systems under Rician fading channels”, IEICE    Trans. Fundamentals, vol. E91-A, no. 10, pp. 2798-2807, October    2008.-   Non-Patent Literature 4: “Turbo space-time codes with time varying    linear transformations”, IEEE Trans. Wireless communications, vol.    6, no. 2, pp. 486-493, February 2007.-   Non-Patent Literature 5: “Likelihood function for QR-MLD suitable    for soft-decision turbo decoding and its performance”, IEICE Trans.    Commun., vol. E88-B, no. 1, pp. 47-57, January 2004.-   Non-Patent Literature 6: “A tutorial on ‘parallel concatenated    (Turbo) coding’, ‘Turbo (iterative) decoding’ and related topics”,    The Institute of Electronics, Information, and Communication    Engineers, Technical Report IT 98-51.-   Non-Patent Literature 7: “Advanced signal processing for PLCs:    Wavelet-OFDM”, Proc. of IEEE International symposium on ISPLC 2008,    pp. 187-192, 2008.-   Non-Patent Literature 8: D. J. Love, and R. W. Heath, Jr., “Limited    feedback unitary precoding for spatial multiplexing systems”, IEEE    Trans. Inf. Theory, vol. 51, no. 8, pp. 2967-2976, August 2005.-   Non-Patent Literature 9: DVB Document A122, Framing structure,    channel coding and modulation for a second generation digital    terrestrial television broadcasting system, (DVB-T2), June 2008.-   Non-Patent Literature 10: L. Vangelista, N. Benvenuto, and S.    Tomasin, “Key technologies for next-generation terrestrial digital    television standard DVB-T2”, IEEE Commun. Magazine, vol. 47, no. 10,    pp. 146-153, October 2009.-   Non-Patent Literature 11: T. Ohgane, T. Nishimura, and Y. Ogawa,    “Application of space division multiplexing and those performance in    a MIMO channel”, IEICE Trans. Commun., vol. E88-B, no. 5, pp.    1843-1851, May 2005.-   Non-Patent Literature 12: R. G. Gallager, “Low-density parity-check    codes”, IRE Trans. Inform. Theory, IT-8, pp. 21-28, 1962.-   Non-Patent Literature 13: D. J. C. Mackay, “Good error-correcting    codes based on very sparse matrices”, IEEE Trans. Inform. Theory,    vol. 45, no. 2, pp. 399-431, March 1999.-   Non-Patent Literature 14: ETSI EN 302307, “Second generation framing    structure, channel coding and modulation systems for broadcasting,    interactive services, news gathering and other broadband satellite    applications”, v. 1.1.2, June 2006.-   Non-Patent Literature 15: Y.-L. Ueng, and C.-C. Cheng, “A    fast-convergence decoding method and memory-efficient VLSI decoder    architecture for irregular LDPC codes in the IEEE 802.16e    standards”, IEEE VTC-2007 Fall, pp. 1255-1259.

SUMMARY OF INVENTION Technical Problem

It is an object of the present invention to provide a MIMO system thatimproves reception quality in an LOS environment.

Solution to Problem

To solve the above problem, the present invention provides a precodingmethod for generating, from a plurality of signals which are based on aselected modulation scheme and represented by in-phase components andquadrature components, a plurality of precoded signals that aretransmitted in the same frequency bandwidth at the same time andtransmitting the generated precoded signals, the precoding methodcomprising: selecting one precoding weight matrix from among a pluralityof precoding weight matrices by regularly hopping between the matrices;and generating the plurality of precoded signals by multiplying theselected precoding weight matrix by the plurality of signals which arebased on the selected modulation scheme, the plurality of precodingweight matrices being nine matrices expressed, using a positive realnumber a, as Equations 339 through 347 (details are described below).

According to each aspect of the above invention, precoded signals, whichare generated by precoding signals by using one precoding weight matrixselected from among a plurality of precoding weight matrices byregularly hopping between the matrices, are transmitted and received.Thus the precoding weight matrix used in the precoding is any of aplurality of precoding weight matrices that have been predetermined.This makes it possible to improve the reception quality in an LOSenvironment based on the design of the plurality of precoding weightmatrices.

Advantageous Effects of Invention

With the above structure, the present invention provides a precodingmethod, a precoding device, a transmission method, a reception method, atransmission device, and a reception device that remedy degradation ofreception quality in an LOS environment, thereby providing high-qualityservice to LOS users during broadcast or multicast communication.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is an example of the structure of a transmission device and areception device in a spatial multiplexing MIMO system.

FIG. 2 is an example of a frame structure.

FIG. 3 is an example of the structure of a transmission device whenadopting a scheme of hopping between precoding weights.

FIG. 4 is an example of the structure of a transmission device whenadopting a scheme of hopping between precoding weights.

FIG. 5 is an example of a frame structure.

FIG. 6 is an example of a scheme of hopping between precoding weights.

FIG. 7 is an example of the structure of a reception device.

FIG. 8 is an example of the structure of a signal processing unit in areception device.

FIG. 9 is an example of the structure of a signal processing unit in areception device.

FIG. 10 shows a decoding processing scheme.

FIG. 11 is an example of reception conditions.

FIGS. 12A and 12B are examples of BER characteristics.

FIG. 13 is an example of the structure of a transmission device whenadopting a scheme of hopping between precoding weights.

FIG. 14 is an example of the structure of a transmission device whenadopting a scheme of hopping between precoding weights.

FIGS. 15A and 15B are examples of a frame structure.

FIGS. 16A and 16B are examples of a frame structure.

FIGS. 17A and 17B are examples of a frame structure.

FIGS. 18A and 18B are examples of a frame structure.

FIGS. 19A and 19B are examples of a frame structure.

FIG. 20 shows positions of poor reception quality points.

FIG. 21 shows positions of poor reception quality points.

FIG. 22 is an example of a frame structure.

FIG. 23 is an example of a frame structure.

FIGS. 24A and 24B are examples of mapping schemes.

FIGS. 25A and 25B are examples of mapping schemes.

FIG. 26 is an example of the structure of a weighting unit.

FIG. 27 is an example of a scheme for reordering symbols.

FIG. 28 is an example of the structure of a transmission device and areception device in a spatial multiplexing MIMO system.

FIGS. 29A and 29B are examples of BER characteristics.

FIG. 30 is an example of a 2×2 MIMO spatial multiplexing MIMO system.

FIGS. 31A and 31B show positions of poor reception points.

FIG. 32 shows positions of poor reception points.

FIGS. 33A and 33B show positions of poor reception points.

FIG. 34 shows positions of poor reception points.

FIGS. 35A and 35B show positions of poor reception points.

FIG. 36 shows an example of minimum distance characteristics of poorreception points in an imaginary plane.

FIG. 37 shows an example of minimum distance characteristics of poorreception points in an imaginary plane.

FIGS. 38A and 38B show positions of poor reception points.

FIGS. 39A and 39B show positions of poor reception points.

FIG. 40 is an example of the structure of a transmission device inEmbodiment 7.

FIG. 41 is an example of the frame structure of a modulated signaltransmitted by the transmission device.

FIGS. 42A and 42B show positions of poor reception points.

FIGS. 43A and 43B show positions of poor reception points.

FIGS. 44A and 44B show positions of poor reception points.

FIGS. 45A and 45B show positions of poor reception points.

FIGS. 46A and 46B show positions of poor reception points.

FIGS. 47A and 47B are examples of a frame structure in the time andfrequency domains.

FIGS. 48A and 48B are examples of a frame structure in the time andfrequency domains.

FIG. 49 shows a signal processing scheme.

FIG. 50 shows the structure of modulated signals when using space-timeblock coding.

FIG. 51 is a detailed example of a frame structure in the time andfrequency domains.

FIG. 52 is an example of the structure of a transmission device.

FIG. 53 is an example of a structure of the modulated signal generatingunits #1-#M in FIG. 52.

FIG. 54 shows the structure of the OFDM related processors (5207_1 and5207_2) in FIG. 52.

FIGS. 55A and 55B are detailed examples of a frame structure in the timeand frequency domains.

FIG. 56 is an example of the structure of a reception device.

FIG. 57 shows the structure of the OFDM related processors (5600_X and5600Y) in FIG. 56.

FIGS. 58A and 58B are detailed examples of a frame structure in the timeand frequency domains.

FIG. 59 is an example of a broadcasting system.

FIGS. 60A and 60B show positions of poor reception points.

FIG. 61 is an example of the frame structure.

FIG. 62 is an example of a frame structure in the time and frequencydomain.

FIG. 63 is an example of a structure of a transmission device.

FIG. 64 is an example of a frame structure in the frequency and timedomain.

FIG. 65 is an example of the frame structure.

FIG. 66 is an example of symbol arrangement scheme.

FIG. 67 is an example of symbol arrangement scheme.

FIG. 68 is an example of symbol arrangement scheme.

FIG. 69 is an example of the frame structure.

FIG. 70 shows a frame structure in the time and frequency domain.

FIG. 71 is an example of a frame structure in the time and frequencydomain.

FIG. 72 is an example of a structure of a transmission device.

FIG. 73 is an example of a structure of a reception device.

FIG. 74 is an example of a structure of a reception device.

FIG. 75 is an example of a structure of a reception device.

FIGS. 76A and 76B show examples of a frame structure in a frequency-timedomain.

FIGS. 77A and 77B show examples of a frame structure in a frequency-timedomain.

FIGS. 78A and 78B show a result of allocating precoding matrices.

FIGS. 79A and 79B show a result of allocating precoding matrices.

FIGS. 80A and 80B show a result of allocating precoding matrices.

FIG. 81 is an example of the structure of a signal processing unit.

FIG. 82 is an example of the structure of a signal processing unit.

FIG. 83 is an example of the structure of the transmission device.

FIG. 84 shows the overall structure of a digital broadcasting system.

FIG. 85 is a block diagram showing an example of the structure of areception device.

FIG. 86 shows the structure of multiplexed data.

FIG. 87 schematically shows how each stream is multiplexed in themultiplexed data.

FIG. 88 shows in more detail how a video stream is stored in a sequenceof PES packets.

FIG. 89 shows the structure of a TS packet and a source packet inmultiplexed data.

FIG. 90 shows the data structure of a PMT.

FIG. 91 shows the internal structure of multiplexed data information.

FIG. 92 shows the internal structure of stream attribute information.

FIG. 93 is a structural diagram of a video display and an audio outputdevice.

FIG. 94 is an example of signal point layout for 16QAM.

FIG. 95 is an example of signal point layout for QPSK.

FIG. 96 shows a baseband signal hopping unit.

FIG. 97 shows the number of symbols and the number of slots.

FIG. 98 shows the number of symbols and the number of slots.

FIGS. 99A and 99B each show a structure of a frame structure.

FIG. 100 shows the number of slots.

FIG. 101 shows the number of shots.

FIG. 102 shows a PLP in the time and frequency domain.

FIG. 103 shows a structure of the PLP.

FIG. 104 shows a PLP in the time and frequency domain.

DESCRIPTION OF EMBODIMENTS

The following describes embodiments of the present invention withreference to the drawings.

Embodiment 1

The following describes the transmission scheme, transmission device,reception scheme, and reception device of the present embodiment.

Prior to describing the present embodiment, an overview is provided of atransmission scheme and decoding scheme in a conventional spatialmultiplexing MIMO system.

FIG. 1 shows the structure of an N_(t)×N_(r) spatial multiplexing MIMOsystem.

An information vector z is encoded and interleaved. As output of theinterleaving, an encoded bit vector u=(u₁, . . . , u_(Nt)) is acquired.Note that u_(i)=(u_(i1), . . . , u_(iM)) (where M is the number oftransmission bits per symbol). Letting the transmission vector s=(s₁, .. . , s_(Nt))^(T) and the transmission signal from transmit antenna #1be represented as s_(i)=map(u_(i)), the normalized transmission energyis represented as E{|s_(i)|²}=Es/Nt (E_(s) being the total energy perchannel). Furthermore, letting the received vector be y=(y₁, . . . ,y_(Nr))^(T), the received vector is represented as in Equation 1.

Math 1

$\begin{matrix}\begin{matrix}{y = \left( {y_{1},\ldots\mspace{14mu},y_{Nr}} \right)^{T}} \\{= {{H_{NtNr}s} + n}}\end{matrix} & {{Equation}\mspace{14mu} 1}\end{matrix}$

In this Equation, H_(NtNr) is the channel matrix, n=(n₁, . . . ,n_(Nr))^(T) is the noise vector, and n_(i) is the i.i.d. complexGaussian random noise with an average value 0 and variance σ². From therelationship between transmission symbols and reception symbols that isinduced at the reception device, the probability for the received vectormay be provided as a multi-dimensional Gaussian distribution, as inEquation 2.

Math 2

$\begin{matrix}{{p\left( y \middle| u \right)} = {\frac{1}{\left( {2\pi\;\sigma^{2}} \right)^{N_{r}}}{\exp\left( {{- \frac{1}{2\sigma^{2}}}{{y - {{Hs}(u)}}}^{2}} \right)}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

Here, a reception device that performs iterative decoding composed of anouter soft-in/soft-out decoder and a MIMO detector, as in FIG. 1, isconsidered. The vector of a log-likelihood ratio (L-value) in FIG. 1 isrepresented as in Equations 3-5.

Math 3L(u)=(L(u ₁), . . . ,L(u _(N) _(t) )^(T)  Equation 3Math 4L(u _(i))=(L(u _(i1)), . . . ,L(u _(iM))  Equation 4Math 5

$\begin{matrix}{{L\left( u_{ij} \right)} = {\ln\;\frac{P\left( {u_{ij} = {+ 1}} \right)}{P\left( {u_{ij} = {- 1}} \right)}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$<Iterative Detection Scheme>

The following describes iterative detection of MIMO signals in theN_(t)×N_(r) spatial multiplexing MIMO system.

The log-likelihood ratio of u_(mn) is defined as in Equation 6.

Math 6

$\begin{matrix}{{L\left( u_{mn} \middle| y \right)} = {\ln\;\frac{P\left( {u_{mn} = \left. {+ 1} \middle| y \right.} \right)}{P\left( {u_{mn} = \left. {- 1} \middle| y \right.} \right)}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

From Bayes' theorem, Equation 6 can be expressed as Equation 7.

Math 7

$\begin{matrix}\begin{matrix}{{L\left( u_{mn} \middle| y \right)} = {\ln\;\frac{{p\left( {\left. y \middle| u_{mn} \right. = {+ 1}} \right)}{{P\left( {u_{mn} = {+ 1}} \right)}/{p(y)}}}{{p\left( {\left. y \middle| u_{mn} \right. = {- 1}} \right)}{{P\left( {u_{mn} = {- 1}} \right)}/{p(y)}}}}} \\{= {{\ln\;\frac{P\left( {u_{mn} = {+ 1}} \right)}{P\left( {u_{mn} = {- 1}} \right)}} + {\ln\;\frac{p\left( {\left. y \middle| u_{mn} \right. = {+ 1}} \right)}{p\left( {\left. y \middle| u_{mn} \right. = {- 1}} \right)}}}} \\{= {{\ln\;\frac{P\left( {u_{mn} = {+ 1}} \right)}{P\left( {u_{mn} = {- 1}} \right)}} + {\ln\;\frac{\sum_{U_{{mn},{+ 1}}}{{p\left( y \middle| u \right)}{p\left( u \middle| u_{mn} \right)}}}{\sum_{U_{{mn},{- 1}}}{{p\left( y \middle| u \right)}{p\left( u \middle| u_{mn} \right)}}}}}}\end{matrix} & {{Equation}\mspace{14mu} 7}\end{matrix}$

Let U_(mn,±1)={u|u_(mn)=±1}. When approximating ln Σa_(j)˜max ln a_(j),an approximation of Equation 7 can be sought as Equation 8. Note thatthe above symbol “˜” indicates approximation.

Math 8

$\begin{matrix}{{L\left( u_{mn} \middle| y \right)} \approx {{\ln\;\frac{P\left( {u_{mn} = {+ 1}} \right)}{P\left( {u_{mn} = {- 1}} \right)}} + {\max\limits_{{Umn},{+ 1}}\left\{ {{\ln\;{p\left( y \middle| u \right)}} + {P\left( u \middle| u_{mn} \right)}} \right\}} - {\max\limits_{{Umn},{- 1}}\left\{ {{\ln\;{p\left( y \middle| u \right)}} + {P\left( u \middle| u_{mn} \right)}} \right\}}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

P(u|u_(mn)) and ln P(u|u_(mn)) in Equation 8 are represented as follows.

Math 9

$\begin{matrix}\begin{matrix}{{P\left( u \middle| u_{mn} \right)} = {\prod\limits_{{({ij})} \neq {({mn})}}{P\left( u_{ij} \right)}}} \\{= {\prod\limits_{{({ij})} \neq {({mn})}}\frac{\exp\left( \frac{u_{ij}{L\left( u_{ij} \right)}}{2} \right)}{{\exp\left( \frac{L\left( u_{ij} \right)}{2} \right)} + {\exp\left( {- \frac{L\left( u_{ij} \right)}{2}} \right)}}}}\end{matrix} & {{Equation}\mspace{14mu} 9}\end{matrix}$Math 10

$\begin{matrix}{{\ln\;{P\left( u \middle| u_{mn} \right)}} = {\left( {\sum\limits_{ij}{\ln\;{P\left( u_{ij} \right)}}} \right) - {\ln\;{P\left( u_{mn} \right)}}}} & {{Equation}\mspace{14mu} 10}\end{matrix}$Math 11

$\begin{matrix}\begin{matrix}{{\ln\;{P\left( u_{ij} \right)}} = {{\frac{1}{2}u_{ij}{P\left( u_{ij} \right)}} - {\ln\left( {{\exp\left( \frac{L\left( u_{ij} \right)}{2} \right)} + {\exp\left( {- \frac{L\left( u_{ij} \right)}{2}} \right)}} \right)}}} \\{\approx {{\frac{1}{2}u_{ij}{L\left( u_{ij} \right)}} - {\frac{1}{2}{{L\left( u_{ij} \right)}}\mspace{14mu}{for}\mspace{14mu}{{L\left( u_{ij} \right)}}}} > 2} \\{= {{\frac{L\left( u_{ij} \right)}{2}}\left( {{u_{ij}{{sign}\left( {L\left( u_{ij} \right)} \right)}} - 1} \right)}}\end{matrix} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Incidentally, the logarithmic probability of the equation defined inEquation 2 is represented in Equation 12.

Math 12

$\begin{matrix}{{\ln\;{P\left( y \middle| u \right)}} = {{{- \frac{N_{r}}{2}}{\ln\left( {2\pi\;\sigma^{2}} \right)}} - {\frac{1}{2\sigma^{2}}{{y - {{Hs}(u)}}}^{2}}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

Accordingly, from Equations 7 and 13, in MAP or A Posteriori Probability(APP), the a posteriori L-value is represented as follows.

Math 13

$\begin{matrix}{{L\left( u_{mn} \middle| y \right)} = {\ln\;\frac{\sum_{U_{{mn},{+ 1}}}{\exp\left\{ {{{- \frac{1}{2\sigma^{2}}}{{y - {{Hs}(u)}}}^{2}} + {\sum\limits_{ij}{\ln\;{P\left( u_{ij} \right)}}}} \right\}}}{\sum_{U_{{mn},{- 1}}}{\exp\left\{ {{{- \frac{1}{2\sigma^{2\;}}}{{y - {{Hs}(u)}}}^{2}} + {\sum\limits_{ij}{\ln\;{P\left( u_{ij} \right)}}}}\; \right\}}}}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

Hereinafter, this is referred to as iterative APP decoding. FromEquations 8 and 12, in the log-likelihood ratio utilizing Max-Logapproximation (Max-Log APP), the a posteriori L-value is represented asfollows.

Math 14

$\begin{matrix}{{L\left( u_{mn} \middle| y \right)} \approx {{\max\limits_{{Umn},{+ 1}}\left\{ {\Psi\left( {u,y,{L(u)}} \right)} \right\}} - {\max\limits_{{Umn},{- 1}}\left\{ {\Psi\left( {u,y,{L(u)}} \right)} \right\}}}} & {{Equation}\mspace{14mu} 14}\end{matrix}$Math 15

$\begin{matrix}{{\Psi\left( {u,y,{L(u)}} \right)} = {{{- \frac{1}{2\sigma^{2}}}{{y - {{Hs}(u)}}}^{2}} + {\sum\limits_{ij}{\ln\;{P\left( u_{ij} \right)}}}}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

Hereinafter, this is referred to as iterative Max-log APP decoding. Theextrinsic information required in an iterative decoding system can besought by subtracting prior inputs from Equations 13 and 14.

<System Model>

FIG. 28 shows the basic structure of the system that is related to thesubsequent description. This system is a 2×2 spatial multiplexing MIMOsystem. There is an outer encoder for each of streams A and B. The twoouter encoders are identical LDPC encoders. (Here, a structure usingLDPC encoders as the outer encoders is described as an example, but theerror correction coding used by the outer encoder is not limited to LDPCcoding. The present invention may similarly be embodied using othererror correction coding such as turbo coding, convolutional coding, LDPCconvolutional coding, and the like. Furthermore, each outer encoder isdescribed as having a transmit antenna, but the outer encoders are notlimited to this structure. A plurality of transmit antennas may be used,and the number of outer encoders may be one. Also, a greater number ofouter encoders may be used than the number of transmit antennas.) Thestreams A and B respectively have interleavers (π_(a), π_(b)). Here, themodulation scheme is 2^(h)-QAM (with h bits transmitted in one symbol).

The reception device performs iterative detection on the above MIMOsignals (iterative APP (or iterative Max-log APP) decoding). Decoding ofLDPC codes is performed by, for example, sum-product decoding.

FIG. 2 shows a frame structure and lists the order of symbols afterinterleaving. In this case, (i_(a), j_(a)), (i_(b), j_(b)) arerepresented by the following Equations.

Math 16(i _(a) ,j _(a))=π_(a)(Ω_(ia,ja) ^(a))  Equation 16Math 17(i _(b) ,j _(b))=π_(b)(Ω_(ib,jb) ^(a))  Equation 17

In this case, i^(a), i^(b) indicate the order of symbols afterinterleaving, j^(a), j^(b) indicate the bit positions (j^(a), j^(b)=1, .. . , h) in the modulation scheme, π^(a), π^(b) indicate theinterleavers for the streams A and B, and Ω^(a) _(ia,ja), Ω^(b) _(ib,jb)indicate the order of data in streams A and B before interleaving. Notethat FIG. 2 shows the frame structure for i_(a)=i_(b).

<Iterative Decoding>

The following is a detailed description of the algorithms forsum-product decoding used in decoding of LDPC codes and for iterativedetection of MIMO signals in the reception device.

Sum-Product Decoding

Let a two-dimensional M×N matrix H={H_(mn)} be the check matrix for LDPCcodes that are targeted for decoding. Subsets A(m), B(n) of the set [1,N]={1, 2, . . . , N} are defined by the following Equations.

Math 18A(m)≡{n:H _(mn)=1}  Equation 18Math 19B(n)≡{m:H _(mn)≡1}  Equation 19

In these Equations, A(m) represents the set of column indices of 1's inthe m^(th) column of the check matrix H, and B(n) represents the set ofrow indices of 1's in the n^(th) row of the check matrix H. Thealgorithm for sum-product decoding is as follows.

Step A•1 (initialization): let a priori value log-likelihood ratioβ_(mn)=0 for all combinations (m, n) satisfying H_(mn)=1. Assume thatthe loop variable (the number of iterations) 1_(sum)=1 and the maximumnumber of loops is set to 1_(sum,max).

Step A•2 (row processing): the extrinsic value log-likelihood ratioα_(mn) is updated for all combinations (m, n) satisfying H_(mn)=1 in theorder of m=1, 2, . . . , M, using the following updating Equations.

Math 20

$\begin{matrix}{\alpha_{mn} = {\left( {\prod\limits_{n^{\prime} \in {{A{(m)}}\backslash\; n}}{{sign}\left( {\lambda_{n^{\prime}} + \beta_{{mn}^{\prime}}} \right)}} \right) \times {f\left( {\sum\limits_{n^{\prime} \in {{A{(m)}}\backslash\; n}}{f\left( {\lambda_{n^{\prime}} + \beta_{{mn}^{\prime}}} \right)}} \right)}}} & {{Equation}\mspace{14mu} 20}\end{matrix}$Math 21

$\begin{matrix}{{{sign}(x)} \equiv \left\{ \begin{matrix}1 & {x \geq 0} \\{- 1} & {x < 0}\end{matrix} \right.} & {{Equation}\mspace{14mu} 21}\end{matrix}$Math 22

$\begin{matrix}{{f(x)} \equiv {\ln\;\frac{{\exp(x)} + 1}{{\exp(x)} - 1}}} & {{Equation}\mspace{14mu} 22}\end{matrix}$

In these Equations, f represents a Gallager function. Furthermore, thescheme of seeking λ_(n) is described in detail later.

Step A•3 (column processing): the extrinsic value log-likelihood ratioβ_(mn) is updated for all combinations (m, n) satisfying H_(mn)=1 in theorder of n=1, 2, . . . , N, using the following updating Equation.

Math 23

$\begin{matrix}{\beta_{mn} = {\sum\limits_{m^{\prime} \in {{B{(n)}}\backslash\; m}}\alpha_{m^{\prime}n}}} & {{Equation}\mspace{14mu} 23}\end{matrix}$Step A•4 (calculating a log-likelihood ratio): the log-likelihood ratioL_(n) is sought for nε[1, N] by the following Equation.Math 24

$\begin{matrix}{L_{n} = {{\sum\limits_{m^{\prime} \in {{B{(n)}}\backslash\; m}}\alpha_{m^{\prime}n}} + \lambda_{n}}} & {{Equation}\mspace{14mu} 24}\end{matrix}$Step A•5 (count of the number of iterations): if 1_(sum)<1_(sum, max),then 1_(sum) is incremented, and processing returns to step A•2. If1_(sum)=1_(sum, max), the sum-product decoding in this round isfinished.

The operations in one sum-product decoding have been described.Subsequently, iterative MIMO signal detection is performed. In thevariables m, n, α_(mn), β_(mn), λ_(n), and L_(n), used in the abovedescription of the operations of sum-product decoding, the variables instream A are m_(a), n_(a), α^(a) _(mana), β^(a) _(mana), λ_(na), andL_(na), and the variables in stream B are m_(b), n_(b), α^(b) _(mbnb),β^(b) _(mbnb), λ_(nb), and L_(nb).

<Iterative MIMO Signal Detection>

The following describes the scheme of seeking λ_(n) in iterative MIMOsignal detection in detail.

The following Equation holds from Equation 1.

Math 25

$\begin{matrix}\begin{matrix}{{y(t)} = \left( {{y_{1}(t)},{y_{2}(t)}} \right)^{T}} \\{= {{{H_{22}(t)}{s(t)}} + {n(t)}}}\end{matrix} & {{Equation}\mspace{14mu} 25}\end{matrix}$

The following Equations are defined from the frame structures of FIG. 2and from Equations 16 and 17.

Math 26n _(a)=Ω_(ia,ja) ^(a)  Equation 26Math 27n _(b)=Ω_(ib,jb) ^(b)  Equation 27

In this case, n_(a), n_(b)ε[1, N]. Hereinafter, λ_(na), L_(na), λ_(nb),and L_(nb), where the number of iterations of iterative MIMO signaldetection is k, are represented as λ_(k, na), L_(k, na), λ_(k, nb), andL_(k, nb).

Step B•1 (initial detection; k=0): λ_(0, na) and λ_(0, nb) are sought asfollows in the case of initial detection.

In iterative APP decoding:

Math 28

$\begin{matrix}{\lambda_{0,_{n_{X}}} = {\ln\frac{\sum_{U_{0,_{n_{X},{+ 1}}}}{\exp\left\{ {{- \frac{1}{2\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}} \right\}}}{\sum_{U_{0,_{n_{X},{- 1}}}}{\exp\left\{ {{- \frac{1}{2\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}} \right\}}}}} & {{Equation}\mspace{14mu} 28}\end{matrix}$

In iterative Max-log APP decoding:

Math 29

$\begin{matrix}{\lambda_{0,_{n_{X}}} = {{\max\limits_{U_{o,_{n_{X},{+ 1}}}}\left\{ {\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)}} \right)} \right\}} - {\max\limits_{U_{0,_{n_{X},{- 1}}}}\left\{ {\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)}} \right)} \right\}}}} & {{Equation}\mspace{14mu} 29}\end{matrix}$Math 30

$\begin{matrix}{{\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)}} \right)} = {{- \frac{1}{2\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}}} & {{Equation}\mspace{14mu} 30}\end{matrix}$

Here, let X=a, b. Then, assume that the number of iterations ofiterative MIMO signal detection is 1_(mimo)=0 and the maximum number ofiterations is set to 1_(mimo, max).

Step B•2 (iterative detection; the number of iterations k): λ_(k, na)and λ_(k, nb), where the number of iterations is k, are represented asin Equations 31-34, from Equations 11, 13-15, 16, and 17. Let (X, Y)=(a,b)(b, a).

In iterative APP decoding:

Math 31

                                      Equation  31$\lambda_{k,_{n_{X}}} = {{L_{{k - 1},\Omega_{{iX},{jX}}^{X}}\left( u_{\Omega_{{iX},{jX}}^{X}} \right)} + {\ln\frac{\sum\limits_{U_{k,n_{X},{+ 1}}}{\exp\left\{ {{{- \frac{1}{2\;\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}} + {\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}} \right\}}}{\sum\limits_{U_{k,n_{X},{- 1}}}{\exp\left\{ {{{- \frac{1}{2\;\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}} + {\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}} \right\}}}}}$Math 32

                                      Equation  32${\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)} = {{\sum\limits_{\underset{\gamma \neq {jX}}{\gamma = 1}}^{h}{{\frac{L_{{k - 1},\Omega_{{iX},\gamma}^{X}}\left( u_{\Omega_{{iX},\gamma}^{X}} \right)}{2}}\left( {{u_{\Omega_{{iX},\gamma}^{X}}{{sign}\left( {L_{{k - 1},\Omega_{{iX},\gamma}^{X}}\left( u_{\Omega_{{iX},\gamma}^{X}} \right)} \right)}} - 1} \right)}} + {\sum\limits_{\gamma = 1}^{h}{{\frac{L_{{k - 1},\Omega_{{iX},\gamma}^{X}}\left( u_{\Omega_{{iX},\gamma}^{X}} \right)}{2}}\left( {{u_{\Omega_{{iX},\gamma}^{X}}{{sign}\left( {L_{{k - 1},\Omega_{{iX},\gamma}^{X}}\left( u_{\Omega_{{iX},\gamma}^{X}} \right)} \right)}} - 1} \right)}}}$

In iterative Max-log APP decoding:

Math 33

$\begin{matrix}{\lambda_{k,_{n_{X}}} = {{L_{{k - 1},\Omega_{{iX},{jX}}^{X}}\left( u_{\Omega_{{iX},{jX}}^{X}} \right)} + {\max\limits_{U_{k,{n_{X,} + 1}}}\left\{ {\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)},{\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}} \right)} \right\}} - {\max\limits_{U_{k,n_{X},{- 1}}}\left\{ {\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)},{\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}} \right)} \right\}}}} & {{Equation}\mspace{14mu} 33}\end{matrix}$Math 34

$\begin{matrix}{{\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)},{\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}} \right)} = {{{- \frac{1}{2\;\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}} + {\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}}} & {{Equation}\mspace{14mu} 34}\end{matrix}$

Step B•3 (counting the number of iterations and estimating a codeword):increment 1_(mimo) if 1_(mimo)<1_(mimo, max), and return to step B•2.Assuming that 1_(mimo)=1_(mimo, max), the estimated codeword is soughtas in the following Equation.

Math 35

$\begin{matrix}{{\hat{u}}_{n_{X}} = \left\{ \begin{matrix}1 & {L_{l_{mimo},n_{X}} \geq 0} \\{- 1} & {L_{l_{mimo},n_{X}} < 0}\end{matrix} \right.} & {{Equation}\mspace{14mu} 35}\end{matrix}$

Here, let X=a, b.

FIG. 3 is an example of the structure of a transmission device 300 inthe present embodiment. An encoder 302A receives information (data) 301Aand a frame structure signal 313 as inputs and, in accordance with theframe structure signal 313, performs error correction coding such asconvolutional coding, LDPC coding, turbo coding, or the like, outputtingencoded data 303A. (The frame structure signal 313 includes informationsuch as the error correction scheme used for error correction coding ofdata, the coding rate, the block length, and the like. The encoder 302Auses the error correction scheme indicated by the frame structure signal313. Furthermore, the error correction scheme may be hopped.)

An interleaver 304A receives the encoded data 303A and the framestructure signal 313 as inputs and performs interleaving, i.e. changingthe order of the data, to output interleaved data 305A. (The scheme ofinterleaving may be hopped based on the frame structure signal 313.)

A mapping unit 306A receives the interleaved data 305A and the framestructure signal 313 as inputs, performs modulation such as QuadraturePhase Shift Keying (QPSK), 16 Quadrature Amplitude Modulation (16QAM),64 Quadrature Amplitude Modulation (64QAM), or the like, and outputs aresulting baseband signal 307A. (The modulation scheme may be hoppedbased on the frame structure signal 313.)

FIGS. 24A and 24B are an example of a mapping scheme over an I-Q plane,having an in-phase component I and a quadrature component Q, to form abaseband signal in QPSK modulation. For example, as shown in FIG. 24A,if the input data is “00”, the output is I=1.0, Q=1.0. Similarly, forinput data of “01”, the output is I=−1.0, Q=1.0, and so forth. FIG. 24Bis an example of a different scheme of mapping in an I-Q plane for QPSKmodulation than FIG. 24A. The difference between FIG. 24B and FIG. 24Ais that the signal points in FIG. 24A have been rotated around theorigin to yield the signal points of FIG. 24B. Non-Patent Literature 9and Non-Patent Literature 10 describe such a constellation rotationscheme, and the Cyclic Q Delay described in Non-Patent Literature 9 andNon-Patent Literature 10 may also be adopted. As another example apartfrom FIGS. 24A and 24B, FIGS. 25A and 25B show signal point layout inthe I-Q plane for 16QAM. The example corresponding to FIG. 24A is shownin FIG. 25A, and the example corresponding to FIG. 24B is shown in FIG.25B.

An encoder 302B receives information (data) 301B and the frame structuresignal 313 as inputs and, in accordance with the frame structure signal313, performs error correction coding such as convolutional coding, LDPCcoding, turbo coding, or the like, outputting encoded data 303B. (Theframe structure signal 313 includes information such as the errorcorrection scheme used, the coding rate, the block length, and the like.The error correction scheme indicated by the frame structure signal 313is used. Furthermore, the error correction scheme may be hopped.)

An interleaver 304B receives the encoded data 303B and the framestructure signal 313 as inputs and performs interleaving, i.e. changingthe order of the data, to output interleaved data 305B. (The scheme ofinterleaving may be hopped based on the frame structure signal 313.)

A mapping unit 306B receives the interleaved data 305B and the framestructure signal 313 as inputs, performs modulation such as QuadraturePhase Shift Keying (QPSK), 16 Quadrature Amplitude Modulation (16QAM),64 Quadrature Amplitude Modulation (64QAM), or the like, and outputs aresulting baseband signal 307B. (The modulation scheme may be hoppedbased on the frame structure signal 313.)

A weighting information generating unit 314 receives the frame structuresignal 313 as an input and outputs information 315 regarding a weightingscheme based on the frame structure signal 313. The weighting scheme ischaracterized by regular hopping between weights.

A weighting unit 308A receives the baseband signal 307A, the basebandsignal 307B, and the information 315 regarding the weighting scheme, andbased on the information 315 regarding the weighting scheme, performsweighting on the baseband signal 307A and the baseband signal 307B andoutputs a signal 309A resulting from the weighting. Details on theweighting scheme are provided later.

A wireless unit 310A receives the signal 309A resulting from theweighting as an input and performs processing such as orthogonalmodulation, band limiting, frequency conversion, amplification, and thelike, outputting a transmission signal 311A. A transmission signal 511Ais output as a radio wave from an antenna 312A.

A weighting unit 308B receives the baseband signal 307A, the basebandsignal 307B, and the information 315 regarding the weighting scheme, andbased on the information 315 regarding the weighting scheme, performsweighting on the baseband signal 307A and the baseband signal 307B andoutputs a signal 309B resulting from the weighting.

FIG. 26 shows the structure of a weighting unit. The baseband signal307A is multiplied by w11(t), yielding w11(t)s1(t), and is multiplied byw21(t), yielding w21(t)s1(t). Similarly, the baseband signal 307B ismultiplied by w12(t) to generate w12(t)s2(t) and is multiplied by w22(t)to generate w22(t)s2(t). Next, z1(t)=w11(t)s1(t)+w12(t)s2(t) andz2(t)=w21(t)s1(t)+w22(t)s2(t) are obtained.

Details on the weighting scheme are provided later.

A wireless unit 310B receives the signal 309B resulting from theweighting as an input and performs processing such as orthogonalmodulation, band limiting, frequency conversion, amplification, and thelike, outputting a transmission signal 311B. A transmission signal 511Bis output as a radio wave from an antenna 312B.

FIG. 4 shows an example of the structure of a transmission device 400that differs from FIG. 3. The differences in FIG. 4 from FIG. 3 aredescribed.

An encoder 402 receives information (data) 401 and the frame structuresignal 313 as inputs and, in accordance with the frame structure signal313, performs error correction coding and outputs encoded data 402.

A distribution unit 404 receives the encoded data 403 as an input,distributes the data 403, and outputs data 405A and data 405B. Note thatin FIG. 4, one encoder is shown, but the number of encoders is notlimited in this way. The present invention may similarly be embodiedwhen the number of encoders is m (where m is an integer greater than orequal to one) and the distribution unit divides encoded data generatedby each encoder into two parts and outputs the divided data.

FIG. 5 shows an example of a frame structure in the time domain for atransmission device according to the present embodiment. A symbol 500_1is a symbol for notifying the reception device of the transmissionscheme. For example, the symbol 500_1 conveys information such as theerror correction scheme used for transmitting data symbols, the codingrate, and the modulation scheme used for transmitting data symbols.

The symbol 501_1 is for estimating channel fluctuation for the modulatedsignal z1(t) (where t is time) transmitted by the transmission device.The symbol 502_1 is the data symbol transmitted as symbol number u (inthe time domain) by the modulated signal z1(t), and the symbol 503_1 isthe data symbol transmitted as symbol number u+1 by the modulated signalz1(t).

The symbol 501_2 is for estimating channel fluctuation for the modulatedsignal z2(t) (where t is time) transmitted by the transmission device.The symbol 502_2 is the data symbol transmitted as symbol number u bythe modulated signal z2(t), and the symbol 503_2 is the data symboltransmitted as symbol number u+1 by the modulated signal z2(t).

The following describes the relationships between the modulated signalsz1(t) and z2(t) transmitted by the transmission device and the receivedsignals r1(t) and r2(t) received by the reception device.

In FIG. 5, 504#1 and 504#2 indicate transmit antennas in thetransmission device, and 505#1 and 505#2 indicate receive antennas inthe reception device. The transmission device transmits the modulatedsignal z1(t) from transmit antenna 504#1 and transmits the modulatedsignal z2(t) from transmit antenna 504#2. In this case, the modulatedsignal z1(t) and the modulated signal z2(t) are assumed to occupy thesame (a shared/common) frequency (bandwidth). Letting the channelfluctuation for the transmit antennas of the transmission device and theantennas of the reception device be h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t),the signal received by the receive antenna 505#1 of the reception devicebe r1(t), and the signal received by the receive antenna 505#2 of thereception device be r2(t), the following relationship holds.

Math 36

$\begin{matrix}{\begin{pmatrix}{r\; 1(t)} \\{r\; 2(t)}\end{pmatrix} = {\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z\; 1(t)} \\{z\; 2(t)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 36}\end{matrix}$

FIG. 6 relates to the weighting scheme (precoding scheme) in the presentembodiment. A weighting unit 600 integrates the weighting units 308A and308B in FIG. 3. As shown in FIG. 6, a stream s1(t) and a stream s2(t)correspond to the baseband signals 307A and 307B in FIG. 3. In otherwords, the streams s1(t) and s2(t) are the baseband signal in-phasecomponents I and quadrature components Q when mapped according to amodulation scheme such as QPSK, 16QAM, 64QAM, or the like. As indicatedby the frame structure of FIG. 6, the stream s1(t) is represented ass1(u) at symbol number u, as s1(u+1) at symbol number u+1, and so forth.Similarly, the stream s2(t) is represented as s2(u) at symbol number u,as s2(u+1) at symbol number u+1, and so forth. The weighting unit 600receives the baseband signals 307A (s1(t)) and 307B (s2(t)) and theinformation 315 regarding weighting information in FIG. 3 as inputs,performs weighting in accordance with the information 315 regardingweighting, and outputs the signals 309A (z1(t)) and 309B (z2(t)) afterweighting in FIG. 3. In this case, z1(t) and z2(t) are represented asfollows.

For symbol number 4i (where i is an integer greater than or equal tozero):

Math 37

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {4i} \right)} \\{z\; 2\left( {4i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\frac{3}{4}\pi}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {4i} \right)} \\{s\; 2\left( {4i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 37}\end{matrix}$Here, j is an imaginary unit.For symbol number 4i+1:Math 38

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{4i} + 1} \right)} \\{z\; 2\left( {{4i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\frac{3}{4}\pi} & {\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 1} \right)} \\{s\; 2\left( {{4i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 38}\end{matrix}$Math 39

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{4i} + 2} \right)} \\{z\; 2\left( {{4i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\frac{3}{4}\pi} \\{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 2} \right)} \\{s\; 2\left( {{4i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 39}\end{matrix}$For symbol number 4i+3:Math 40

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{4i} + 3} \right)} \\{z\; 2\left( {{4i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\frac{3}{4}\pi} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 3} \right)} \\{s\; 2\left( {{4i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 40}\end{matrix}$

In this way, the weighting unit in FIG. 6 regularly hops betweenprecoding weights over a four-slot period (cycle). (While precodingweights have been described as being hopped between regularly over fourslots, the number of slots for regular hopping is not limited to four.)

Incidentally, Non-Patent Literature 4 describes hopping the precodingweights for each slot. This hopping of precoding weights ischaracterized by being random. On the other hand, in the presentembodiment, a certain period (cycle) is provided, and the precodingweights are hopped between regularly. Furthermore, in each 2×2 precodingweight matrix composed of four precoding weights, the absolute value ofeach of the four precoding weights is equivalent to (1/sqrt(2)), andhopping is regularly performed between precoding weight matrices havingthis characteristic.

In an LOS environment, if a special precoding matrix is used, receptionquality may greatly improve, yet the special precoding matrix differsdepending on the conditions of direct waves. In an LOS environment,however, a certain tendency exists, and if precoding matrices are hoppedbetween regularly in accordance with this tendency, the receptionquality of data greatly improves. On the other hand, when precodingmatrices are hopped between at random, a precoding matrix other than theabove-described special precoding matrix may exist, and the possibilityof performing precoding only with biased precoding matrices that are notsuitable for the LOS environment also exists. Therefore, in an LOSenvironment, excellent reception quality may not always be obtained.Accordingly, there is a need for a precoding hopping scheme suitable foran LOS environment. The present invention proposes such a precodingscheme.

FIG. 7 is an example of the structure of a reception device 700 in thepresent embodiment. A wireless unit 703_X receives, as an input, areceived signal 702_X received by an antenna 701_X, performs processingsuch as frequency conversion, quadrature demodulation, and the like, andoutputs a baseband signal 704_X.

A channel fluctuation estimating unit 705_1 for the modulated signal z1transmitted by the transmission device receives the baseband signal704_X as an input, extracts a reference symbol 501_1 for channelestimation as in FIG. 5, estimates a value corresponding to h₁₁ inEquation 36, and outputs a channel estimation signal 706_1.

A channel fluctuation estimating unit 705_2 for the modulated signal z2transmitted by the transmission device receives the baseband signal704_X as an input, extracts a reference symbol 501_2 for channelestimation as in FIG. 5, estimates a value corresponding to h₁₂ inEquation 36, and outputs a channel estimation signal 706_2.

A wireless unit 703_Y receives, as input, a received signal 702_Yreceived by an antenna 701_Y, performs processing such as frequencyconversion, quadrature demodulation, and the like, and outputs abaseband signal 704_Y.

A channel fluctuation estimating unit 707_1 for the modulated signal z1transmitted by the transmission device receives the baseband signal704_Y as an input, extracts a reference symbol 501_1 for channelestimation as in FIG. 5, estimates a value corresponding to h₂₁ inEquation 36, and outputs a channel estimation signal 708_1.

A channel fluctuation estimating unit 707_2 for the modulated signal z2transmitted by the transmission device receives the baseband signal704_Y as an input, extracts a reference symbol 501_2 for channelestimation as in FIG. 5, estimates a value corresponding to h₂₂ inEquation 36, and outputs a channel estimation signal 708_2.

A control information decoding unit 709 receives the baseband signal704_X and the baseband signal 704_Y as inputs, detects the symbol 500_1that indicates the transmission scheme as in FIG. 5, and outputs asignal 710 regarding information on the transmission scheme indicated bythe transmission device.

A signal processing unit 711 receives, as inputs, the baseband signals704_X and 704_Y, the channel estimation signals 706_1, 706_2, 708_1, and708_2, and the signal 710 regarding information on the transmissionscheme indicated by the transmission device, performs detection anddecoding, and outputs received data 712_1 and 712_2.

Next, operations by the signal processing unit 711 in FIG. 7 aredescribed in detail. FIG. 8 is an example of the structure of the signalprocessing unit 711 in the present embodiment. FIG. 8 shows an INNERMIMO detector, a soft-in/soft-out decoder, and a weighting coefficientgenerating unit as the main elements. Non-Patent Literature 2 andNon-Patent Literature 3 describe the scheme of iterative decoding withthis structure. The MIMO system described in Non-Patent Literature 2 andNon-Patent Literature 3 is a spatial multiplexing MIMO system, whereasthe present embodiment differs from Non-Patent Literature 2 andNon-Patent Literature 3 by describing a MIMO system that changesprecoding weights with time. Letting the (channel) matrix in Equation 36be H(t), the precoding weight matrix in FIG. 6 be W(t) (where theprecoding weight matrix changes over t), the received vector beR(t)=(r1(t),r2(t))^(T), and the stream vector be S(t)=(s1(t),s2(t))^(T),the following Equation holds.

Math 41R(t)=H(t)W(t)S(t)  Equation 41

In this case, the reception device can apply the decoding scheme inNon-Patent Literature 2 and Non-Patent Literature 3 to the receivedvector R(t) by considering H(t)W(t) as the channel matrix.

Therefore, a weighting coefficient generating unit 819 in FIG. 8receives, as input, a signal 818 regarding information on thetransmission scheme indicated by the transmission device (correspondingto 710 in FIG. 7) and outputs a signal 820 regarding information onweighting coefficients.

An INNER MIMO detector 803 receives the signal 820 regarding informationon weighting coefficients as input and, using the signal 820, performsthe calculation in Equation 41. Iterative detection and decoding is thusperformed. The following describes operations thereof.

In the signal processing unit in FIG. 8, a processing scheme such asthat shown in FIG. 10 is necessary for iterative decoding (iterativedetection). First, one codeword (or one frame) of the modulated signal(stream) s1 and one codeword (or one frame) of the modulated signal(stream) s2 are decoded. As a result, the Log-Likelihood Ratio (LLR) ofeach bit of the one codeword (or one frame) of the modulated signal(stream) s1 and of the one codeword (or one frame) of the modulatedsignal (stream) s2 is obtained from the soft-in/soft-out decoder.Detection and decoding is performed again using the LLR. Theseoperations are performed multiple times (these operations being referredto as iterative decoding (iterative detection)). Hereinafter,description focuses on the scheme of generating the log-likelihood ratio(LLR) of a symbol at a particular time in one frame.

In FIG. 8, a storage unit 815 receives, as inputs, a baseband signal801X (corresponding to the baseband signal 704_X in FIG. 7), a channelestimation signal group 802X (corresponding to the channel estimationsignals 706_1 and 706_2 in FIG. 7), a baseband signal 801Y(corresponding to the baseband signal 704_Y in FIG. 7), and a channelestimation signal group 802Y (corresponding to the channel estimationsignals 708_1 and 708_2 in FIG. 7). In order to achieve iterativedecoding (iterative detection), the storage unit 815 calculates H(t)W(t)in Equation 41 and stores the calculated matrix as a transformed channelsignal group. The storage unit 815 outputs the above signals whennecessary as a baseband signal 816X, a transformed channel estimationsignal group 817X, a baseband signal 816Y, and a transformed channelestimation signal group 817Y.

Subsequent operations are described separately for initial detection andfor iterative decoding (iterative detection).

<Initial Detection>

The INNER MIMO detector 803 receives, as inputs, the baseband signal801X, the channel estimation signal group 802X, the baseband signal801Y, and the channel estimation signal group 802Y. Here, the modulationscheme for the modulated signal (stream) s1 and the modulated signal(stream) s2 is described as 16QAM.

The INNER MIMO detector 803 first calculates H(t)W(t) from the channelestimation signal group 802X and the channel estimation signal group802Y to seek candidate signal points corresponding to the basebandsignal 801X. FIG. 11 shows such calculation. In FIG. 11, each black dot(•) is a candidate signal point in the I-Q plane. Since the modulationscheme is 16QAM, there are 256 candidate signal points. (Since FIG. 11is only for illustration, not all 256 candidate signal points areshown.) Here, letting the four bits transferred by modulated signal s1be b0, b1, b2, and b3, and the four bits transferred by modulated signals2 be b4, b5, b6, and b7, candidate signal points corresponding to (b0,b1, b2, b3, b4, b5, b6, b7) in FIG. 11 exist. The squared Euclidiandistance is sought between a received signal point 1101 (correspondingto the baseband signal 801X) and each candidate signal point. Eachsquared Euclidian distance is divided by the noise variance σ².Accordingly, E_(X)(b0, b1, b2, b3, b4, b5, b6, b7), i.e. the value ofthe squared Euclidian distance between a candidate signal pointcorresponding to (b0, b1, b2, b3, b4, b5, b6, b7) and a received signalpoint, divided by the noise variance, is sought. Note that the basebandsignals and the modulated signals s1 and s2 are each complex signals.

Similarly, H(t)W(t) is calculated from the channel estimation signalgroup 802X and the channel estimation signal group 802Y, candidatesignal points corresponding to the baseband signal 801Y are sought, thesquared Euclidian distance for the received signal point (correspondingto the baseband signal 801Y) is sought, and the squared Euclidiandistance is divided by the noise variance σ². Accordingly, E_(Y)(b0, b1,b2, b3, b4, b5, b6, b7), i.e. the value of the squared Euclidiandistance between a candidate signal point corresponding to (b0, b1, b2,b3, b4, b5, b6, b7) and a received signal point, divided by the noisevariance, is sought.

Then E_(X)(b0, b1, b2, b3, b4, b5, b6, b7)+E_(Y)(b0, b1, b2, b3, b4, b5,b6, b7)=E(b0, b1, b2, b3, b4, b5, b6, b7) is sought.

The INNER MIMO detector 803 outputs E(b0, b1, b2, b3, b4, b5, b6, b7) asa signal 804.

A log-likelihood calculating unit 805A receives the signal 804 as input,calculates the log likelihood for bits b0, b1, b2, and b3, and outputs alog-likelihood signal 806A. Note that during calculation of the loglikelihood, the log likelihood for “1” and the log likelihood for “0”are calculated. The calculation scheme is as shown in Equations 28, 29,and 30. Details can be found in Non-Patent Literature 2 and Non-PatentLiterature 3.

Similarly, a log-likelihood calculating unit 805B receives the signal804 as input, calculates the log likelihood for bits b4, b5, b6, and b7,and outputs a log-likelihood signal 806B.

A deinterleaver (807A) receives the log-likelihood signal 806A as aninput, performs deinterleaving corresponding to the interleaver (theinterleaver (304A) in FIG. 3), and outputs a deinterleavedlog-likelihood signal 808A.

Similarly, a deinterleaver (807B) receives the log-likelihood signal806B as an input, performs deinterleaving corresponding to theinterleaver (the interleaver (304B) in FIG. 3), and outputs adeinterleaved log-likelihood signal 808B.

A log-likelihood ratio calculating unit 809A receives the interleavedlog-likelihood signal 808A as an input, calculates the log-likelihoodratio (LLR) of the bits encoded by the encoder 302A in FIG. 3, andoutputs a log-likelihood ratio signal 810A.

Similarly, a log-likelihood ratio calculating unit 809B receives theinterleaved log-likelihood signal 808B as an input, calculates thelog-likelihood ratio (LLR) of the bits encoded by the encoder 302B inFIG. 3, and outputs a log-likelihood ratio signal 810B.

A soft-in/soft-out decoder 811A receives the log-likelihood ratio signal810A as an input, performs decoding, and outputs a decodedlog-likelihood ratio 812A.

Similarly, a soft-in/soft-out decoder 811B receives the log-likelihoodratio signal 810B as an input, performs decoding, and outputs a decodedlog-likelihood ratio 812B.

<Iterative Decoding (Iterative Detection), Number of Iterations k>

An interleaver (813A) receives the log-likelihood ratio 812A decoded bythe soft-in/soft-out decoder in the (k−₁)^(th) iteration as an input,performs interleaving, and outputs an interleaved log-likelihood ratio814A. The interleaving pattern in the interleaver (813A) is similar tothe interleaving pattern in the interleaver (304A) in FIG. 3.

An interleaver (813B) receives the log-likelihood ratio 812B decoded bythe soft-in/soft-out decoder in the (k−1)^(th) iteration as an input,performs interleaving, and outputs an interleaved log-likelihood ratio814B. The interleaving pattern in the interleaver (813B) is similar tothe interleaving pattern in the interleaver (304B) in FIG. 3.

The INNER MIMO detector 803 receives, as inputs, the baseband signal816X, the transformed channel estimation signal group 817X, the basebandsignal 816Y, the transformed channel estimation signal group 817Y, theinterleaved log-likelihood ratio 814A, and the interleavedlog-likelihood ratio 814B. The reason for using the baseband signal816X, the transformed channel estimation signal group 817X, the basebandsignal 816Y, and the transformed channel estimation signal group 817Yinstead of the baseband signal 801X, the channel estimation signal group802X, the baseband signal 801Y, and the channel estimation signal group802Y is because a delay occurs due to iterative decoding.

The difference between operations by the INNER MIMO detector 803 foriterative decoding and for initial detection is the use of theinterleaved log-likelihood ratio 814A and the interleaved log-likelihoodratio 814B during signal processing. The INNER MIMO detector 803 firstseeks E(b0, b1, b2, b3, b4, b5, b6, b7), as during initial detection.Additionally, coefficients corresponding to Equations 11 and 32 aresought from the interleaved log-likelihood ratio 814A and theinterleaved log-likelihood ratio 914B. The value E(b0, b1, b2, b3, b4,b5, b6, b7) is adjusted using the sought coefficients, and the resultingvalue E′(b0, b1, b2, b3, b4, b5, b6, b7) is output as the signal 804.

The log-likelihood calculating unit 805A receives the signal 804 asinput, calculates the log likelihood for bits b0, b1, b2, and b3, andoutputs the log-likelihood signal 806A. Note that during calculation ofthe log likelihood, the log likelihood for “1” and the log likelihoodfor “0” are calculated. The calculation scheme is as shown in Equations31, 32, 33, 34, and 35. Details can be found in Non-Patent Literature 2and Non-Patent Literature 3.

Similarly, the log-likelihood calculating unit 805B receives the signal804 as input, calculates the log likelihood for bits b4, b5, b6, and b7,and outputs the log-likelihood signal 806B. Operations by thedeinterleaver onwards are similar to initial detection.

Note that while FIG. 8 shows the structure of the signal processing unitwhen performing iterative detection, iterative detection is not alwaysessential for obtaining excellent reception quality, and a structure notincluding the interleavers 813A and 813B, which are necessary only foriterative detection, is possible. In such a case, the INNER MIMOdetector 803 does not perform iterative detection.

The main part of the present embodiment is calculation of H(t)W(t). Notethat as shown in Non-Patent Literature 5 and the like, QR decompositionmay be used to perform initial detection and iterative detection.

Furthermore, as shown in Non-Patent Literature 11, based on H(t)W(t),linear operation of the Minimum Mean Squared Error (MMSE) and ZeroForcing (ZF) may be performed in order to perform initial detection.

FIG. 9 is the structure of a different signal processing unit than FIG.8 and is for the modulated signal transmitted by the transmission devicein FIG. 4. The difference with FIG. 8 is the number of soft-in/soft-outdecoders. A soft-in/soft-out decoder 901 receives, as inputs, thelog-likelihood ratio signals 810A and 810B, performs decoding, andoutputs a decoded log-likelihood ratio 902. A distribution unit 903receives the decoded log-likelihood ratio 902 as an input anddistributes the log-likelihood ratio 902. Other operations are similarto FIG. 8.

FIGS. 12A and 12B show BER characteristics for a transmission schemeusing the precoding weights of the present embodiment under similarconditions to FIGS. 29A and 29B. FIG. 12A shows the BER characteristicsof Max-log A Posteriori Probability (APP) without iterative detection(see Non-Patent Literature 1 and Non-Patent Literature 2), and FIG. 12Bshows the BER characteristics of Max-log-APP with iterative detection(see Non-Patent Literature 1 and Non-Patent Literature 2) (number ofiterations: five). Comparing FIGS. 12A, 12B, 29A, and 29B shows how ifthe transmission scheme of the present embodiment is used, the BERcharacteristics when the Rician factor is large greatly improve over theBER characteristics when using spatial multiplexing MIMO system, therebyconfirming the usefulness of the scheme in the present embodiment.

As described above, when a transmission device transmits a plurality ofmodulated signals from a plurality of antennas in a MIMO system, theadvantageous effect of improved transmission quality, as compared toconventional spatial multiplexing MIMO system, is achieved in an LOSenvironment in which direct waves dominate by hopping between precodingweights regularly over time, as in the present embodiment.

In the present embodiment, and in particular with regards to thestructure of the reception device, operations have been described for alimited number of antennas, but the present invention may be embodied inthe same way even if the number of antennas increases. In other words,the number of antennas in the reception device does not affect theoperations or advantageous effects of the present embodiment.Furthermore, in the present embodiment, the example of LDPC coding hasparticularly been explained, but the present invention is not limited toLDPC coding. Furthermore, with regards to the decoding scheme, thesoft-in/soft-out decoders are not limited to the example of sum-productdecoding. Another soft-in/soft-out decoding scheme may be used, such asa BCJR algorithm, a SOVA algorithm, a Max-log-MAP algorithm, and thelike. Details are provided in Non-Patent Literature 6.

Additionally, in the present embodiment, the example of a single carrierscheme has been described, but the present invention is not limited inthis way and may be similarly embodied for multi-carrier transmission.Accordingly, when using a scheme such as spread spectrum communication,Orthogonal Frequency-Division Multiplexing (OFDM), Single CarrierFrequency Division Multiple Access (SC-FDMA), Single Carrier OrthogonalFrequency-Division Multiplexing (SC-OFDM), or wavelet OFDM as describedin Non-Patent Literature 7 and the like, for example, the presentinvention may be similarly embodied. Furthermore, in the presentembodiment, symbols other than data symbols, such as pilot symbols(preamble, unique word, and the like), symbols for transmission ofcontrol information, and the like, may be arranged in the frame in anyway.

The following describes an example of using OFDM as an example of amulti-carrier scheme.

FIG. 13 shows the structure of a transmission device when using OFDM. InFIG. 13, elements that operate in a similar way to FIG. 3 bear the samereference signs.

An OFDM related processor 1301A receives, as input, the weighted signal309A, performs processing related to OFDM, and outputs a transmissionsignal 1302A. Similarly, an OFDM related processor 1301B receives, asinput, the weighted signal 309B, performs processing related to OFDM,and outputs a transmission signal 1302B.

FIG. 14 shows an example of a structure from the OFDM related processors1301A and 1301B in FIG. 13 onwards. The part from 1401A to 1410A isrelated to the part from 1301A to 312A in FIG. 13, and the part from1401B to 1410B is related to the part from 1301B to 312B in FIG. 13.

A serial/parallel converter 1402A performs serial/parallel conversion ona weighted signal 1401A (corresponding to the weighted signal 309A inFIG. 13) and outputs a parallel signal 1403A.

A reordering unit 1404A receives a parallel signal 1403A as input,performs reordering, and outputs a reordered signal 1405A. Reordering isdescribed in detail later.

An inverse fast Fourier transformer 1406A receives the reordered signal1405A as an input, performs a fast Fourier transform, and outputs a fastFourier transformed signal 1407A.

A wireless unit 1408A receives the fast Fourier transformed signal 1407Aas an input, performs processing such as frequency conversion,amplification, and the like, and outputs a modulated signal 1409A. Themodulated signal 1409A is output as a radio wave from an antenna 1410A.

A serial/parallel converter 1402B performs serial/parallel conversion ona weighted signal 1401B (corresponding to the weighted signal 309B inFIG. 13) and outputs a parallel signal 1403B.

A reordering unit 1404B receives a parallel signal 1403B as input,performs reordering, and outputs a reordered signal 1405B. Reordering isdescribed in detail later.

An inverse fast Fourier transformer 1406B receives the reordered signal1405B as an input, performs a fast Fourier transform, and outputs a fastFourier transformed signal 1407B.

A wireless unit 1408B receives the fast Fourier transformed signal 1407Bas an input, performs processing such as frequency conversion,amplification, and the like, and outputs a modulated signal 1409B. Themodulated signal 1409B is output as a radio wave from an antenna 1410B.

In the transmission device of FIG. 3, since the transmission scheme doesnot use multi-carrier, precoding hops to form a four-slot period(cycle), as shown in FIG. 6, and the precoded symbols are arranged inthe time domain. When using a multi-carrier transmission scheme as inthe OFDM scheme shown in FIG. 13, it is of course possible to arrangethe precoded symbols in the time domain as in FIG. 3 for each(sub)carrier. In the case of a multi-carrier transmission scheme,however, it is possible to arrange symbols in the frequency domain, orin both the frequency and time domains. The following describes thesearrangements.

FIGS. 15A and 15B show an example of a scheme of reordering symbols byreordering units 1401A and 1401B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time. Thefrequency domain runs from (sub)carrier 0 through (sub)carrier 9. Themodulated signals z1 and z2 use the same frequency bandwidth at the sametime. FIG. 15A shows the reordering scheme for symbols of the modulatedsignal z1, and FIG. 15B shows the reordering scheme for symbols of themodulated signal z2. Numbers #1, #2, #3, #4, . . . are assigned to inorder to the symbols of the weighted signal 1401A which is input intothe serial/parallel converter 1402A. At this point, symbols are assignedregularly, as shown in FIG. 15A. The symbols #1, #2, #3, #4, . . . arearranged in order starting from carrier 0. The symbols #1 through #9 areassigned to time $1, and subsequently, the symbols #10 through #19 areassigned to time $2.

Similarly, numbers #1, #2, #3, #4, . . . are assigned in order to thesymbols of the weighted signal 1401B which is input into theserial/parallel converter 1402B. At this point, symbols are assignedregularly, as shown in FIG. 15B. The symbols #1, #2, #3, #4, . . . arearranged in order starting from carrier 0. The symbols #1 through #9 areassigned to time $1, and subsequently, the symbols #10 through #19 areassigned to time $2. Note that the modulated signals z1 and z2 arecomplex signals.

The symbol group 1501 and the symbol group 1502 shown in FIGS. 15A and15B are the symbols for one period (cycle) when using the precodingweight hopping scheme shown in FIG. 6. Symbol #0 is the symbol whenusing the precoding weight of slot 4i in FIG. 6. Symbol #1 is the symbolwhen using the precoding weight of slot 4i+1 in FIG. 6. Symbol #2 is thesymbol when using the precoding weight of slot 4i+2 in FIG. 6. Symbol #3is the symbol when using the precoding weight of slot 4i+3 in FIG. 6.Accordingly, symbol #x is as follows. When x mod 4 is 0, the symbol #xis the symbol when using the precoding weight of slot 4i in FIG. 6. Whenx mod 4 is 1, the symbol #x is the symbol when using the precodingweight of slot 4i+1 in FIG. 6. When x mod 4 is 2, the symbol #x is thesymbol when using the precoding weight of slot 4i+2 in FIG. 6. When xmod 4 is 3, the symbol #x is the symbol when using the precoding weightof slot 4i+3 in FIG. 6.

In this way, when using a multi-carrier transmission scheme such asOFDM, unlike during single carrier transmission, symbols can be arrangedin the frequency domain. Furthermore, the ordering of symbols is notlimited to the ordering shown in FIGS. 15A and 15B. Other examples aredescribed with reference to FIGS. 16A, 16B, 17A, and 17B.

FIGS. 16A and 16B show an example of a scheme of reordering symbols bythe reordering units 1404A and 1404B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time, thatdiffers from FIGS. 15A and 15B. FIG. 16A shows the reordering scheme forsymbols of the modulated signal z1, and FIG. 16B shows the reorderingscheme for symbols of the modulated signal z2. The difference in FIGS.16A and 16B as compared to FIGS. 15A and 15B is that the reorderingscheme of the symbols of the modulated signal z1 differs from thereordering scheme of the symbols of the modulated signal z2. In FIG.16B, symbols #0 through #5 are assigned to carriers 4 through 9, andsymbols #6 through #9 are assigned to carriers 0 through 3.Subsequently, symbols #10 through #19 are assigned regularly in the sameway. At this point, as in FIGS. 15A and 15B, the symbol group 1601 andthe symbol group 1602 shown in FIGS. 16A and 16B are the symbols for oneperiod (cycle) when using the precoding weight hopping scheme shown inFIG. 6.

FIGS. 17A and 17B show an example of a scheme of reordering symbols bythe reordering units 1404A and 1404B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time, thatdiffers from FIGS. 15A and 15B. FIG. 17A shows the reordering scheme forsymbols of the modulated signal z1, and FIG. 17B shows the reorderingscheme for symbols of the modulated signal z2. The difference in FIGS.17A and 17B as compared to FIGS. 15A and 15B is that whereas the symbolsare arranged in order by carrier in FIGS. 15A and 15B, the symbols arenot arranged in order by carrier in FIGS. 17A and 17B. It is obviousthat, in FIGS. 17A and 17B, the reordering scheme of the symbols of themodulated signal z1 may differ from the reordering scheme of the symbolsof the modulated signal z2, as in FIGS. 16A and 16B.

FIGS. 18A and 18B show an example of a scheme of reordering symbols bythe reordering units 1404A and 1404B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time, thatdiffers from FIGS. 15A through 17B. FIG. 18A shows the reordering schemefor symbols of the modulated signal z1, and FIG. 18B shows thereordering scheme for symbols of the modulated signal z2. In FIGS. 15Athrough 17B, symbols are arranged in the frequency domain, whereas inFIGS. 18A and 18B, symbols are arranged in both the frequency and timedomains.

In FIG. 6, an example has been described of hopping between precodingweights over four slots. Here, however, an example of hopping over eightslots is described. The symbol groups 1801 and 1802 shown in FIGS. 18Aand 18B are the symbols for one period (cycle) when using the precodingweight hopping scheme (and are therefore eight-symbol groups). Symbol #0is the symbol when using the precoding weight of slot 8i. Symbol #1 isthe symbol when using the precoding weight of slot 8i+1. Symbol #2 isthe symbol when using the precoding weight of slot 8i+2. Symbol #3 isthe symbol when using the precoding weight of slot 8i+3. Symbol #4 isthe symbol when using the precoding weight of slot 8i+4. Symbol #5 isthe symbol when using the precoding weight of slot 8i+5. Symbol #6 isthe symbol when using the precoding weight of slot 8i+6. Symbol #7 isthe symbol when using the precoding weight of slot 8i+7. Accordingly,symbol #x is as follows. When x mod 8 is 0, the symbol #x is the symbolwhen using the precoding weight of slot 8i. When x mod 8 is 1, thesymbol #x is the symbol when using the precoding weight of slot 8i+1.When x mod 8 is 2, the symbol #x is the symbol when using the precodingweight of slot 8i+2. When x mod 8 is 3, the symbol #x is the symbol whenusing the precoding weight of slot 8i+3. When x mod 8 is 4, the symbol#x is the symbol when using the precoding weight of slot 8i+4. When xmod 8 is 5, the symbol #x is the symbol when using the precoding weightof slot 8i+5. When x mod 8 is 6, the symbol #x is the symbol when usingthe precoding weight of slot 8i+6. When x mod 8 is 7, the symbol #x isthe symbol when using the precoding weight of slot 8i+7. In the symbolordering in FIGS. 18A and 18B, four slots in the time domain and twoslots in the frequency domain for a total of 4×2=8 slots are used toarrange symbols for one period (cycle). In this case, letting the numberof symbols in one period (cycle) be m x n symbols (in other words, m x nprecoding weights exist), the number of slots (the number of carriers)in the frequency domain used to arrange symbols in one period (cycle) ben, and the number of slots used in the time domain be m, then m>n shouldbe satisfied. This is because the phase of direct waves fluctuates moreslowly in the time domain than in the frequency domain. Therefore, sincethe precoding weights are changed in the present embodiment to minimizethe influence of steady direct waves, it is preferable to reduce thefluctuation in direct waves in the period (cycle) for changing theprecoding weights. Accordingly, m>n should be satisfied. Furthermore,considering the above points, rather than reordering symbols only in thefrequency domain or only in the time domain, direct waves are morelikely to become stable when symbols are reordered in both the frequencyand the time domains as in FIGS. 18A and 18B, thereby making it easierto achieve the advantageous effects of the present invention. Whensymbols are ordered in the frequency domain, however, fluctuations inthe frequency domain are abrupt, leading to the possibility of yieldingdiversity gain. Therefore, reordering in both the frequency and the timedomains is not necessarily always the best scheme.

FIGS. 19A and 19B show an example of a scheme of reordering symbols bythe reordering units 1404A and 1404B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time, thatdiffers from FIGS. 18A and 18B. FIG. 19A shows the reordering scheme forsymbols of the modulated signal z1, and FIG. 19B shows the reorderingscheme for symbols of the modulated signal z2. As in FIGS. 18A and 18B,FIGS. 19A and 19B show arrangement of symbols using both the frequencyand the time axes. The difference as compared to FIGS. 18A and 18B isthat, whereas symbols are arranged first in the frequency domain andthen in the time domain in FIGS. 18A and 18B, symbols are arranged firstin the time domain and then in the frequency domain in FIGS. 19A and19B. In FIGS. 19A and 19B, the symbol group 1901 and the symbol group1902 are the symbols for one period (cycle) when using the precodinghopping scheme.

Note that in FIGS. 18A, 18B, 19A, and 19B, as in FIGS. 16A and 16B, thepresent invention may be similarly embodied, and the advantageous effectof high reception quality achieved, with the symbol arranging scheme ofthe modulated signal z1 differing from the symbol arranging scheme ofthe modulated signal z2. Furthermore, in FIGS. 18A, 18B, 19A, and 19B,as in FIGS. 17A and 17B, the present invention may be similarlyembodied, and the advantageous effect of high reception qualityachieved, without arranging the symbols in order.

FIG. 27 shows an example of a scheme of reordering symbols by thereordering units 1404A and 1404B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time, thatdiffers from the above examples. The case of hopping between precodingmatrices regularly over four slots, as in Equations 37-40, isconsidered. The characteristic feature of FIG. 27 is that symbols arearranged in order in the frequency domain, but when progressing in thetime domain, symbols are cyclically shifted by n symbols (in the examplein FIG. 27, n=1). In the four symbols shown in the symbol group 2710 inthe frequency domain in FIG. 27, precoding hops between the precodingmatrices of Equations 37-40.

In this case, symbol #0 is precoded using the precoding matrix inEquation 37, symbol #1 is precoded using the precoding matrix inEquation 38, symbol #2 is precoded using the precoding matrix inEquation 39, and symbol #3 is precoded using the precoding matrix inEquation 40.

Similarly, for the symbol group 2720 in the frequency domain, symbol #4is precoded using the precoding matrix in Equation 37, symbol #5 isprecoded using the precoding matrix in Equation 38, symbol #6 isprecoded using the precoding matrix in Equation 39, and symbol #7 isprecoded using the precoding matrix in Equation 40.

For the symbols at time $1, precoding hops between the above precodingmatrices, but in the time domain, symbols are cyclically shifted.Therefore, precoding hops between precoding matrices for the symbolgroups 2701, 2702, 2703, and 2704 as follows.

In the symbol group 2701 in the time domain, symbol #0 is precoded usingthe precoding matrix in Equation 37, symbol #9 is precoded using theprecoding matrix in Equation 38, symbol #18 is precoded using theprecoding matrix in Equation 39, and symbol #27 is precoded using theprecoding matrix in Equation 40.

In the symbol group 2702 in the time domain, symbol #28 is precodedusing the precoding matrix in Equation 37, symbol #1 is precoded usingthe precoding matrix in Equation 38, symbol #10 is precoded using theprecoding matrix in Equation 39, and symbol #19 is precoded using theprecoding matrix in Equation 40.

In the symbol group 2703 in the time domain, symbol #20 is precodedusing the precoding matrix in Equation 37, symbol #29 is precoded usingthe precoding matrix in Equation 38, symbol #2 is precoded using theprecoding matrix in Equation 39, and symbol #11 is precoded using theprecoding matrix in Equation 40.

In the symbol group 2704 in the time domain, symbol #12 is precodedusing the precoding matrix in Equation 37, symbol #21 is precoded usingthe precoding matrix in Equation 38, symbol #30 is precoded using theprecoding matrix in Equation 39, and symbol #3 is precoded using theprecoding matrix in Equation 40.

The characteristic of FIG. 27 is that, for example focusing on symbol#11, the symbols on either side in the frequency domain at the same time(symbols #10 and #12) are both precoded with a different precodingmatrix than symbol #11, and the symbols on either side in the timedomain in the same carrier (symbols #2 and #20) are both precoded with adifferent precoding matrix than symbol #11. This is true not only forsymbol #11. Any symbol having symbols on either side in the frequencydomain and the time domain is characterized in the same way as symbol#11. As a result, precoding matrices are effectively hopped between, andsince the influence on stable conditions of direct waves is reduced, thepossibility of improved reception quality of data increases.

In FIG. 27, the case of n=1 has been described, but n is not limited inthis way. The present invention may be similarly embodied with n=3.Furthermore, in FIG. 27, when symbols are arranged in the frequencydomain and time progresses in the time domain, the above characteristicis achieved by cyclically shifting the number of the arranged symbol,but the above characteristic may also be achieved by randomly (orregularly) arranging the symbols.

Embodiment 2

In Embodiment 1, regular hopping of the precoding weights as shown inFIG. 6 has been described. In the present embodiment, a scheme fordesigning specific precoding weights that differ from the precodingweights in FIG. 6 is described.

In FIG. 6, the scheme for hopping between the precoding weights inEquations 37-40 has been described. By generalizing this scheme, theprecoding weights may be changed as follows. (The hopping period (cycle)for the precoding weights has four slots, and Equations are listedsimilarly to Equations 37-40.)

For symbol number 4i (where i is an integer greater than or equal tozero):

Math 42

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {4i} \right)} \\{z\; 2\left( {4i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({4i})}} & {\mathbb{e}}^{j{({{\theta_{11}{({4i})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({4i})}} & {\mathbb{e}}^{j{({{\theta_{21}{({4i})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {4i} \right)} \\{s\; 2\left( {4i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 42}\end{matrix}$Here, j is an imaginary unit.For symbol number 4i+1:Math 43

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{4i} + 1} \right)} \\{z\; 2\left( {{4i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{4i} + 1})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 1})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{4i} + 1})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 1} \right)} \\{s\; 2\left( {{4i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 43}\end{matrix}$For symbol number 4i+2:Math 44

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{4i} + 2} \right)} \\{z\; 2\left( {{4i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{4i} + 2})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 2})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{4i} + 2})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 2})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 2} \right)} \\{s\; 2\left( {{4i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 44}\end{matrix}$

For symbol number 4i+3:

Math 45

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{4i} + 3} \right)} \\{z\; 2\left( {{4i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{4i} + 3})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 3})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{4i} + 3})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 3})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 3} \right)} \\{s\; 2\left( {{4i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 45}\end{matrix}$From Equations 36 and 41, the received vector R(t)=(r1(t), r2(t))^(T)can be represented as follows.For symbol number 4i:Math 46

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {4i} \right)} \\{r\; 2\left( {4i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{h_{11}\left( {4i} \right)} & {h_{12}\left( {4i} \right)} \\{h_{21}\left( {4i} \right)} & {h_{22}\left( {4i} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({4i})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({4i})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({4i})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({4i})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {4i} \right)} \\{s\; 2\left( {4i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 46}\end{matrix}$For symbol number 4i+1:Math 47

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{4i} + 1} \right)} \\{r\; 2\left( {{4i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{h_{11}\left( {{4i} + 1} \right)} & {h_{12}\left( {{4i} + 1} \right)} \\{h_{21}\left( {{4i} + 1} \right)} & {h_{22}\left( {{4i} + 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4i} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 1})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4i} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 1} \right)} \\{s\; 2\left( {{4i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 47}\end{matrix}$For symbol number 4i+2:Math 48

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{4i} + 2} \right)} \\{r\; 2\left( {{4i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{h_{11}\left( {{4i} + 2} \right)} & {h_{12}\left( {{4i} + 2} \right)} \\{h_{21}\left( {{4i} + 2} \right)} & {h_{22}\left( {{4i} + 2} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4i} + 2})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 2})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4i} + 2})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 2})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 2} \right)} \\{s\; 2\left( {{4i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 48}\end{matrix}$

For symbol number 4i+3:

Math 49

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{4i} + 3} \right)} \\{r\; 2\left( {{4i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{h_{11}\left( {{4i} + 3} \right)} & {h_{12}\left( {{4i} + 3} \right)} \\{h_{21}\left( {{4i} + 3} \right)} & {h_{22}\left( {{4i} + 3} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4i} + 3})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 3})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4i} + 3})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 3})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 3} \right)} \\{s\; 2\left( {{4i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 49}\end{matrix}$

In this case, it is assumed that only components of direct waves existin the channel elements h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t), that theamplitude components of the direct waves are all equal, and thatfluctuations do not occur over time. With these assumptions, Equations46-49 can be represented as follows.

For symbol number 4i:

Math 50

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {4i} \right)} \\{r\; 2\left( {4i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({4i})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({4i})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({4i})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({4i})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {4i} \right)} \\{s\; 2\left( {4i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 50}\end{matrix}$For symbol number 4i+1:Math 51

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{4i} + 1} \right)} \\{r\; 2\left( {{4i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4i} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 1})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4i} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 1} \right)} \\{s\; 2\left( {{4i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 51}\end{matrix}$For symbol number 4i+2:Math 52

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{4i} + 2} \right)} \\{r\; 2\left( {{4i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4i} + 2})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 2})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4i} + 2})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 2})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 2} \right)} \\{s\; 2\left( {{4i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 52}\end{matrix}$For symbol number 4i+3:Math 53

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{4i} + 3} \right)} \\{r\; 2\left( {{4i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4i} + 3})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 3})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4i} + 3})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 3})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 3} \right)} \\{s\; 2\left( {{4i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 53}\end{matrix}$

In Equations 50-53, let A be a positive real number and q be a complexnumber. The values of A and q are determined in accordance with thepositional relationship between the transmission device and thereception device. Equations 50-53 can be represented as follows.

For symbol number 4i:

Math 54

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {4i} \right)} \\{r\; 2\left( {4i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({4i})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({4i})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({4i})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({4i})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {4i} \right)} \\{s\; 2\left( {4i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 54}\end{matrix}$For symbol number 4i+1:Math 55

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{4i} + 1} \right)} \\{r\; 2\left( {{4i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4i} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 1})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4i} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 1} \right)} \\{s\; 2\left( {{4i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 55}\end{matrix}$For symbol number 4i+2:Math 56

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{4i} + 2} \right)} \\{r\; 2\left( {{4i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4i} + 2})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 2})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4i} + 2})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 2})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 2} \right)} \\{s\; 2\left( {{4i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 56}\end{matrix}$For symbol number 4i+3:Math 57

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{4i} + 3} \right)} \\{r\; 2\left( {{4i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2\;}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4i} + 3})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4i} + 3})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4i} + 3})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4i} + 3})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4i} + 3} \right)} \\{s\; 2\left( {{4i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 57}\end{matrix}$

As a result, when q is represented as follows, a signal component basedon one of s1 and s2 is no longer included in r1 and r2, and thereforeone of the signals s1 and s2 can no longer be obtained.

For symbol number 4i:

Math 58q=−A _(e) ^(j(θ) ¹¹ ^((4i)−θ) ²¹ ^((4i)) −A _(e) ^(j(θ) ¹¹ ^((4i)−θ) ²¹^((4i)−δ))  Equation 58For symbol number 4i+1:Math 59q=−A _(e) ^(j(θ) ¹¹ ^((4i+1)−θ) ²¹ ^((4i+1)),) −A _(e) ^(j(θ) ¹¹^((4i+1)−θ) ²¹ ^((4i+1)−δ))  Equation 59For symbol number 4i+2:Math 60q=−A _(e) ^(j(θ) ¹¹ ^((4i+2)−θ) ²¹ ^((4i+2)),) −A _(e) ^(j(θ) ¹¹^((4i+2)−θ) ²¹ ^((4i+2)−δ))  Equation 60For symbol number 4i+3:Math 61q=−A _(e) ^(j(θ) ¹¹ ^((4i+3)−θ) ²¹ ^((4i+3)),) −A _(e) ^(j(θ) ¹¹^((4i+3)−θ) ²¹ ^((4i+3)−δ))  Equation 61

In this case, if q has the same solution in symbol numbers 4i, 4i+1,4i+2, and 4i+3, then the channel elements of the direct waves do notgreatly fluctuate. Therefore, a reception device having channel elementsin which the value of q is equivalent to the same solution can no longerobtain excellent reception quality for any of the symbol numbers.Therefore, it is difficult to achieve the ability to correct errors,even if error correction codes are introduced. Accordingly, for q not tohave the same solution, the following condition is necessary fromEquations 58-61 when focusing on one of two solutions of q which doesnot include δ.

Math 62

Condition #1e ^(j(θ) ¹¹ ^((4i+x)−θ) ²¹ ^((4i+x))) ≠e ^(j(θ) ¹¹ ^((4i+y)−θ) ²¹^((4i+y))) for ∀x,∀y(x≠y;x,y=0,1,2,3)(x is 0, 1, 2, 3; y is 0, 1, 2, 3; and x≠y.)In an example fulfilling Condition #1, values are set as follows:

Example #1

(1) θ₁₁(4i)=θ₁₁(4i+1)=₁₁(4i+2)=θ₁₁(4i+3)=0 radians,

(2) θ₂₁(4i)=0 radians,

(3) θ₂₁(4i+1)=π/2 radians,

(4) θ₂₁(4i+2)=π radians, and

(5) θ₂₁(4i+3)=3π/2 radians.

(The above is an example. It suffices for one each of zero radians, π/2radians, π radians, and 3π/2 radians to exist for the set (θ₂₁(4i),θ₂₁(4i+1), θ₂₁(4i+2), θ₂₁(4i+3)).) In this case, in particular undercondition (1), there is no need to perform signal processing (rotationprocessing) on the baseband signal S1(t), which therefore offers theadvantage of a reduction in circuit size. Another example is to setvalues as follows.

Example #2

(6) θ₁₁(4i)=0 radians,

(7) θ₁₁(4i+1)=π/2 radians,

(8) θ₁₁(4i+2)=π radians,

(9) θ₁₁(4i+3)=3π/2 radians, and

(10) θ₂₁(4i)=θ₂₁(4i+1)=θ₂₁(4i+2)=θ₂₁(4i+3)=0 radians.

(The above is an example. It suffices for one each of zero radians, π/2radians, π radians, and 3π/2 radians to exist for the set (θ₁₁(4i),θ₁₁(4i+1), θ₁₁(4i+2), θ₁₁(4i+3)).) In this case, in particular undercondition (6), there is no need to perform signal processing (rotationprocessing) on the baseband signal S2(t), which therefore offers theadvantage of a reduction in circuit size. Yet another example is asfollows.

Example #3

(11) θ₁₁(4i)=θ₁₁(4i+1)=θ₁₁(4i+2)=θ₁₁(4i+3)=0 radians,

(12) θ₂₁(4i)=0 radians,

(13) θ₂₁(4i+1)=π/4 radians,

(14) θ₂₁(4i+2)=π/2 radians, and

(15) θ₂₁(4i+3)=3π/4 radians.

(The above is an example. It suffices for one each of zero radians, π/4radians, π/2 radians, and 3π/4 radians to exist for the set (θ₂₁(4i),θ₂₁(4i+1), θ₂₁(4i+2), θ₂₁(4i+3)).)

Example #4

(16) θ₁₁(4i)=0 radians,

(17) θ₁₁(4i+1)=π/4 radians,

(18) θ₁₁(4i+2)=π/2 radians,

(19) θ₁₁(4i+3)=3π/4 radians, and

(20) θ₂₁(4i)=θ₂₁(4i+1)=θ₂₁(4i+2)=θ₂₁(4i+3)=0 radians.

(The above is an example. It suffices for one each of zero radians, π/4radians, π/2 radians, and 3π/4 radians to exist for the set (θ₁₁(4i),θ₁₁(4i+1), θ₁₁(4i+2), θ₁₁(4i+3)).)

While four examples have been shown, the scheme of satisfying Condition#1 is not limited to these examples.

Next, design requirements for not only θ₁₁ and θ₁₂, but also for λ and δare described. It suffices to set λ to a certain value; it is thennecessary to establish requirements for δ. The following describes thedesign scheme for δ when λ is set to zero radians.

In this case, by defining δ so that π/2 radians≦|δ|≦π radians, excellentreception quality is achieved, particularly in an LOS environment.

Incidentally, for each of the symbol numbers 4i, 4i+1, 4i+2, and 4i+3,two points q exist where reception quality becomes poor. Therefore, atotal of 2×4=8 such points exist. In an LOS environment, in order toprevent reception quality from degrading in a specific receptionterminal, these eight points should each have a different solution. Inthis case, in addition to Condition #1, Condition #2 is necessary.

Math 63

Condition #2e ^(j(θ) ¹¹ ^((4i+x)−θ) ²¹ ^((4i+x))) ≠e ^(j(θ) ¹¹ ^((4i+y)−θ) ²¹^((4i+y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2,3)ande ^(j(θ) ¹¹ ^((4i+x)−θ) ²¹ ^((4i+x)−δ)) ≠e ^(j(θ) ¹¹ ^((4i+y)−θ) ²¹^((4i+y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2,3)

Additionally, the phase of these eight points should be evenlydistributed (since the phase of a direct wave is considered to have ahigh probability of even distribution). The following describes thedesign scheme for δ to satisfy this requirement.

In the case of example #1 and example #2, the phase becomes even at thepoints at which reception quality is poor by setting δ to ±3π/4 radians.For example, letting δ be 3π/4 radians in example #1 (and letting A be apositive real number), then each of the four slots, points at whichreception quality becomes poor exist once, as shown in FIG. 20. In thecase of example #3 and example #4, the phase becomes even at the pointsat which reception quality is poor by setting δ to ±π radians. Forexample, letting δ be π radians in example #3, then in each of the fourslots, points at which reception quality becomes poor exist once, asshown in FIG. 21. (If the element q in the channel matrix H exists atthe points shown in FIGS. 20 and 21, reception quality degrades.)

With the above structure, excellent reception quality is achieved in anLOS environment. Above, an example of changing precoding weights in afour-slot period (cycle) is described, but below, changing precodingweights in an N-slot period (cycle) is described. Making the sameconsiderations as in Embodiment 1 and in the above description,processing represented as below is performed on each symbol number.

For symbol number Ni (where i is an integer greater than or equal tozero):

Math 64

$\begin{matrix}{\begin{pmatrix}{z\; 1({Ni})} \\{z\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 62}\end{matrix}$Here, j is an imaginary unit.For symbol number Ni+1:Math 65

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{Ni} + 1} \right)} \\{z\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 63}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

Math 66

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{Ni} + k} \right)} \\{z\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 64}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

Math 67

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{Ni} + N - 1} \right)} \\{z\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 65}\end{matrix}$Accordingly, r1 and r2 are represented as follows.For symbol number Ni (where i is an integer greater than or equal tozero):Math 68

$\begin{matrix}{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}({Ni})} & {h_{12}({Ni})} \\{h_{21}({Ni})} & {h_{22}({Ni})}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({Ni})}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 66}\end{matrix}$Here, j is an imaginary unit.For symbol number Ni+1:Math 69

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}\left( {{Ni} + 1} \right)} & {h_{12}\left( {{Ni} + 1} \right)} \\{h_{21}\left( {{Ni} + 1} \right)} & {h_{22}\left( {{Ni} + 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + 1})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 67}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

Math 70

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}\left( {{Ni} + k} \right)} & {h_{12}\left( {{Ni} + k} \right)} \\{h_{21}\left( {{Ni} + k} \right)} & {h_{22}\left( {{Ni} + k} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 68}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

Math 71

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}\left( {{Ni} + N - 1} \right)} & {h_{12}\left( {{Ni} + N - 1} \right)} \\{h_{21}\left( {{Ni} + N - 1} \right)} & {h_{22}\left( {{Ni} + N - 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 69}\end{matrix}$

In this case, it is assumed that only components of direct waves existin the channel elements h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t), that theamplitude components of the direct waves are all equal, and thatfluctuations do not occur over time. With these assumptions, Equations66-69 can be represented as follows.

For symbol number Ni (where i is an integer greater than or equal tozero):

Math 72

$\begin{matrix}{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & q \\{A\;{\mathbb{e}}^{j0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({Ni})}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 70}\end{matrix}$

Here, j is an imaginary unit.

For symbol number Ni+1:

Math 73

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & q \\{A\;{\mathbb{e}}^{j0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + 1})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 71}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

Math 74

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & q \\{A\;{\mathbb{e}}^{j0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 72}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

Math 75

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & q \\{A\;{\mathbb{e}}^{j0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 73}\end{matrix}$

In Equations 70-73, let A be a real number and q be a complex number.The values of A and q are determined in accordance with the positionalrelationship between the transmission device and the reception device.Equations 70-73 can be represented as follows.

For symbol number Ni (where i is an integer greater than or equal tozero):

Math 76

$\begin{matrix}{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\;{\mathbb{e}}^{j0}} \\{\;{\mathbb{e}}^{j0}}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({Ni})}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 74}\end{matrix}$Here, j is an imaginary unit.For symbol number Ni+1:Math 77

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\;{\mathbb{e}}^{j0}} \\{\;{\mathbb{e}}^{j0}}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + 1})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 75}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

Math 78

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\;{\mathbb{e}}^{j0}} \\{\;{\mathbb{e}}^{j0}}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 76}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

Math 79

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\;{\mathbb{e}}^{j0}} \\{\;{\mathbb{e}}^{j0}}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 77}\end{matrix}$

As a result, when q is represented as follows, a signal component basedon one of s1 and s2 is no longer included in r1 and r2, and thereforeone of the signals s1 and s2 can no longer be obtained.

For symbol number Ni (where i is an integer greater than or equal tozero):

Math 80q=−A _(e) ^(j(θ) ¹¹ ^((Ni)−θ) ²¹ ^((Ni))) ,−A _(e) ^(j(θ) ¹¹ ^((Ni)−θ)²¹ ^((Ni)−δ))  Equation 78For symbol number Ni+1:Math 81q=−A _(e) ^(j(θ) ¹¹ ^((Ni+1)−θ) ²¹ ^((Ni+1))) ,−A _(e) ^(j(θ) ¹¹^((Ni+1)−θ) ²¹ ^((Ni+1)−δ))  Equation 79

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

Math 82q=−A _(e) ^(j(θ) ¹¹ ^((Ni+k)−θ) ²¹ ^((Ni+k))) ,−A _(e) ^(j(θ) ¹¹^((Ni+k)−θ) ²¹ ^((Ni+k)−δ))  Equation 80

Furthermore, for symbol number Ni+N−1:

Math 83q=−A _(e) ^(j(θ) ¹¹ ^((Ni+N−1)−θ) ²¹ ^((Ni+N−1))) ,−A _(e) ^(j(θ) ¹¹^((Ni+N−1)−θ) ²¹ ^((Ni+N−1)−δ))  Equation 81

In this case, if q has the same solution in symbol numbers Ni throughNi+N−1, then since the channel elements of the direct waves do notgreatly fluctuate, a reception device having channel elements in whichthe value of q is equivalent to this same solution can no longer obtainexcellent reception quality for any of the symbol numbers. Therefore, itis difficult to achieve the ability to correct errors, even if errorcorrection codes are introduced. Accordingly, for q not to have the samesolution, the following condition is necessary from Equations 78-81 whenfocusing on one of two solutions of q which does not include 6.

Math 84

Condition #3e ^(j(θ) ¹¹ ^((Ni+x)−θ) ²¹ ^((Ni+x))) ≠e ^(j(θ) ¹¹ ^((Ni+y)−θ) ²¹^((Ni+y))) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Next, design requirements for not only θ₁₁ and θ₁₂, but also for λ and δare described. It suffices to set λ to a certain value; it is thennecessary to establish requirements for δ. The following describes thedesign scheme for δ when λ is set to zero radians.

In this case, similar to the scheme of changing the precoding weights ina four-slot period (cycle), by defining δ so that π/2 radians≦|δ|≦πradians, excellent reception quality is achieved, particularly in an LOSenvironment.

In each symbol number Ni through Ni+N−1, two points labeled q existwhere reception quality becomes poor, and therefore 2N such pointsexist. In an LOS environment, in order to achieve excellentcharacteristics, these 2N points should each have a different solution.In this case, in addition to Condition #3, Condition #4 is necessary.

Math 85

Condition #4e ^(j(θ) ¹¹ ^((Ni+x)−θ) ²¹ ^((Ni+x))) ≠e ^(j(θ) ¹¹ ^((Ni+y)−θ) ²¹^((Ni+y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)ande ^(j(θ) ¹¹ ^((Ni+x)−θ) ²¹ ^((Ni+x)−δ)) ≠e ^(j(θ) ¹¹ ^((Ni+y)−θ) ²¹^((Ni+y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

Additionally, the phase of these 2N points should be evenly distributed(since the phase of a direct wave at each reception device is consideredto have a high probability of even distribution).

As described above, when a transmission device transmits a plurality ofmodulated signals from a plurality of antennas in a MIMO system, theadvantageous effect of improved transmission quality, as compared toconventional spatial multiplexing MIMO system, is achieved in an LOSenvironment in which direct waves dominate by hopping between precodingweights regularly over time.

In the present embodiment, the structure of the reception device is asdescribed in Embodiment 1, and in particular with regards to thestructure of the reception device, operations have been described for alimited number of antennas, but the present invention may be embodied inthe same way even if the number of antennas increases. In other words,the number of antennas in the reception device does not affect theoperations or advantageous effects of the present embodiment.Furthermore, in the present embodiment, similar to Embodiment 1, theerror correction codes are not limited.

In the present embodiment, in contrast with Embodiment 1, the scheme ofchanging the precoding weights in the time domain has been described. Asdescribed in Embodiment 1, however, the present invention may besimilarly embodied by changing the precoding weights by using amulti-carrier transmission scheme and arranging symbols in the frequencydomain and the frequency-time domain. Furthermore, in the presentembodiment, symbols other than data symbols, such as pilot symbols(preamble, unique word, and the like), symbols for control information,and the like, may be arranged in the frame in any way.

Embodiment 3

In Embodiment 1 and Embodiment 2, the scheme of regularly hoppingbetween precoding weights has been described for the case where theamplitude of each element in the precoding weight matrix is equivalent.In the present embodiment, however, an example that does not satisfythis condition is described.

For the sake of contrast with Embodiment 2, the case of changingprecoding weights over an N-slot period (cycle) is described. Making thesame considerations as in Embodiment 1 and Embodiment 2, processingrepresented as below is performed on each symbol number. Let β be apositive real number, and β≠1.

For symbol number Ni (where i is an integer greater than or equal tozero):

Math 86

$\begin{matrix}{\begin{pmatrix}{z\; 1({Ni})} \\{z\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 82}\end{matrix}$

Here, j is an imaginary unit.

For symbol number Ni+1:

Math 87

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{Ni} + 1} \right)} \\{z\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 83}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

Math 88

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{Ni} + k} \right)} \\{z\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 84}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

Math 89

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{Ni} + N - 1} \right)} \\{z\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 85}\end{matrix}$

Accordingly, r1 and r2 are represented as follows.

For symbol number Ni (where i is an integer greater than or equal tozero):

Math 90

$\begin{matrix}{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}({Ni})} & {h_{12}({Ni})} \\{h_{21}({Ni})} & {h_{22}({Ni})}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 86}\end{matrix}$

Here, j is an imaginary unit.

For symbol number Ni+1:

Math 91

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{Ni} + 1} \right)} & {h_{12}\left( {{Ni} + 1} \right)} \\{h_{21}\left( {{Ni} + 1} \right)} & {h_{22}\left( {{Ni} + 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 87}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

Math 92

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{Ni} + k} \right)} & {h_{12}\left( {{Ni} + k} \right)} \\{h_{21}\left( {{Ni} + k} \right)} & {h_{22}\left( {{Ni} + k} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 88}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+N−1:

Math 93

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{Ni} + N - 1} \right)} & {h_{12}\left( {{Ni} + N - 1} \right)} \\{h_{21}\left( {{Ni} + N - 1} \right)} & {h_{22}\left( {{Ni} + N - 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 89}\end{matrix}$

In this case, it is assumed that only components of direct waves existin the channel elements h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t), that theamplitude components of the direct waves are all equal, and thatfluctuations do not occur over time. With these assumptions, Equations86-89 can be represented as follows.

For symbol number Ni (where i is an integer greater than or equal tozero):

Math 94

$\begin{matrix}{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{{\, A}\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 90}\end{matrix}$

Here, j is an imaginary unit.

For symbol number Ni+1:

Math 95

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 91}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

Math 96

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 92}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

Math 97

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 93}\end{matrix}$

In Equations 90-93, let A be a real number and q be a complex number.Equations 90-93 can be represented as follows.

For symbol number Ni (where i is an integer greater than or equal tozero):

Math 98

$\begin{matrix}{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 94}\end{matrix}$

Here, j is an imaginary unit.

For symbol number Ni+1:

Math 99

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 95}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

Math 100

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 96}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

Math 101

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 97}\end{matrix}$

As a result, when q is represented as follows, one of the signals s1 ands2 can no longer be obtained.

For symbol number Ni (where i is an integer greater than or equal tozero):

Math 102

$\begin{matrix}{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} - {\theta_{21}{({Ni})}}})}}}},{{- A}\;{\beta\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} - {\theta_{21}{({Ni})}} - \delta})}}}} & {{Equation}\mspace{14mu} 98}\end{matrix}$For symbol number Ni+1:Math 103

$\begin{matrix}{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} - {\theta_{21}{({{Ni} + 1})}}})}}}},{{- A}\;\beta\;{\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} - {\theta_{21}{({{Ni} + 1})}} - \delta})}}}} & {{Equation}\mspace{14mu} 99}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

Math 104

$\begin{matrix}{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{1}{({{Ni} + k})}} - {\theta_{21}{({{Ni} + k})}}})}}}},{{- A}\;\beta\;{\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} - {\theta_{21}{({{Ni} + k})}} - \delta})}}}} & {{Equation}\mspace{14mu} 100}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

Math 105

$\begin{matrix}{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} - {\theta_{21}{({{Ni} + N - 1})}}})}}}},{{- A}\;{\beta\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} - {\theta_{21}{({{Ni} + N - 1})}} - \delta})}}}} & {{Equation}\mspace{14mu} 101}\end{matrix}$

In this case, if q has the same solution in symbol numbers Ni throughNi+N−1, then since the channel elements of the direct waves do notgreatly fluctuate, excellent reception quality can no longer be obtainedfor any of the symbol numbers. Therefore, it is difficult to achieve theability to correct errors, even if error correction codes areintroduced. Accordingly, for q not to have the same solution, thefollowing condition is necessary from Equations 98-101 when focusing onone of two solutions of q which does not include 6.

Math 106

Condition #5e ^(j(θ) ¹¹ ^((Ni+x)−θ) ²¹ ^((Ni+x))) ≠e ^(j(θ) ¹¹ ^((Ni+y)−θ) ²¹^((Ni+y))) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Next, design requirements for not only θ₁, and θ₁₂, but also for λ and δare described. It suffices to set λ to a certain value; it is thennecessary to establish requirements for δ. The following describes thedesign scheme for δ when λ is set to zero radians.

In this case, similar to the scheme of changing the precoding weights ina four-slot period (cycle), by defining δ so that π/2 radians≦|δ|≦πradians, excellent reception quality is achieved, particularly in an LOSenvironment.

In each of symbol numbers Ni through Ni+N−1, two points q exist wherereception quality becomes poor, and therefore 2N such points exist. Inan LOS environment, in order to achieve excellent characteristics, these2N points should each have a different solution. In this case, inaddition to Condition #5, considering that β is a positive real number,and β≠1, Condition #6 is necessary.

Math 107

Condition #6e ^(j(θ) ¹¹ ^((Ni+x)−θ) ²¹ ^((Ni+x)−δ)) ≠e ^(j(θ) ¹¹ ^((Ni+y)−θ) ²¹^((Ni+y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

As described above, when a transmission device transmits a plurality ofmodulated signals from a plurality of antennas in a MIMO system, theadvantageous effect of improved transmission quality, as compared toconventional spatial multiplexing MIMO system, is achieved in an LOSenvironment in which direct waves dominate by hopping between precodingweights regularly over time.

In the present embodiment, the structure of the reception device is asdescribed in Embodiment 1, and in particular with regards to thestructure of the reception device, operations have been described for alimited number of antennas, but the present invention may be embodied inthe same way even if the number of antennas increases. In other words,the number of antennas in the reception device does not affect theoperations or advantageous effects of the present embodiment.

Furthermore, in the present embodiment, similar to Embodiment 1, theerror correction codes are not limited.

In the present embodiment, in contrast with Embodiment 1, the scheme ofchanging the precoding weights in the time domain has been described. Asdescribed in Embodiment 1, however, the present invention may besimilarly embodied by changing the precoding weights by using amulti-carrier transmission scheme and arranging symbols in the frequencydomain and the frequency-time domain. Furthermore, in the presentembodiment, symbols other than data symbols, such as pilot symbols(preamble, unique word, and the like), symbols for control information,and the like, may be arranged in the frame in any way.

Embodiment 4

In Embodiment 3, the scheme of regularly hopping between precodingweights has been described for the example of two types of amplitudesfor each element in the precoding weight matrix, 1 and β.

In this case,

Math 108

$\frac{1}{\sqrt{\beta^{2} + 1}}$is ignored.

Next, the example of changing the value of 3 by slot is described. Forthe sake of contrast with Embodiment 3, the case of changing precodingweights over a 2×N-slot period (cycle) is described.

Making the same considerations as in Embodiment 1, Embodiment 2, andEmbodiment 3, processing represented as below is performed on symbolnumbers. Let β be a positive real number, and β≠1. Furthermore, let α bea positive real number, and α≠β.

For symbol number 2Ni (where i is an integer greater than or equal tozero):

Math 109

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {2{Ni}} \right)} \\{z\; 2\left( {2{Ni}} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({2{Ni}})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({2{Ni}})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({2{Ni}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({2{Ni}})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {2{Ni}} \right)} \\{s\; 2\left( {2{Ni}} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 102}\end{matrix}$Here, j is an imaginary unit.For symbol number 2Ni+1:Math 110

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{2{Ni}} + 1} \right)} \\{z\; 2\left( {{2{Ni}} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + 1} \right)} \\{s\; 2\left( {{2{Ni}} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 103}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+k (k=0, 1, . . . , N−1):

Math 111

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{2{Ni}} + k} \right)} \\{z\; 2\left( {{2{Ni}} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + k} \right)} \\{s\; 2\left( {{2{Ni}} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 104}\end{matrix}$

Furthermore, for symbol number 2Ni+N−1:

Math 112

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{2{Ni}} + N - 1} \right)} \\{z\; 2\left( {{2{Ni}} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N - 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N - 1} \right)} \\{s\; 2\left( {{2{Ni}} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 105}\end{matrix}$For symbol number 2Ni+N (where i is an integer greater than or equal tozero):Math 113

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{2{Ni}} + N} \right)} \\{z\; 2\left( {{2{Ni}} + N} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N} \right)} \\{s\; 2\left( {{2{Ni}} + N} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 106}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+N+1:

Math 114

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{2{Ni}} + N + 1} \right)} \\{z\; 2\left( {{2{Ni}} + N + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N + 1})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N + 1} \right)} \\{s\; 2\left( {{2{Ni}} + N + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 107}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+N+k (k=0, 1, . . . , N−1):

Math 115

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{2{Ni}} + N + k} \right)} \\{z\; 2\left( {{2{Ni}} + N + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N + k})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + k})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N + k} \right)} \\{s\; 2\left( {{2{Ni}} + N + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 108}\end{matrix}$

Furthermore, for symbol number 2Ni+2N−1:

Math 116

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{2{Ni}} + {2N} - 1} \right)} \\{z\; 2\left( {{2{Ni}} + {2N} - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + {2N} - 1})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + {2N} - 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + {2N} - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + {2N} - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + {2N} - 1} \right)} \\{s\; 2\left( {{2{Ni}} + {2N} - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 109}\end{matrix}$

Accordingly, r1 and r2 are represented as follows.

For symbol number 2Ni (where i is an integer greater than or equal tozero):

Math 117

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {2{Ni}} \right)} \\{r\; 2\left( {2{Ni}} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {2{Ni}} \right)} & {h_{12}\left( {2{Ni}} \right)} \\{h_{21}\left( {2{Ni}} \right)} & {h_{22}\left( {2{Ni}} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({2{Ni}})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({2{Ni}})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({2{Ni}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({2{Ni}})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {2{Ni}} \right)} \\{s\; 2\left( {2{Ni}} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 110}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+1:

Math 118

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + 1} \right)} \\{r\; 2\left( {{2{Ni}} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2{Ni}} + 1} \right)} & {h_{12}\left( {{2{Ni}} + 1} \right)} \\{h_{21}\left( {{2{Ni}} + 1} \right)} & {h_{22}\left( {{2{Ni}} + 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + 1} \right)} \\{s\; 2\left( {{2{Ni}} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 111}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+k (k=0, 1, . . . , N−1):

Math 119

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + k} \right)} \\{r\; 2\left( {{2{Ni}} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2{Ni}} + k} \right)} & {h_{12}\left( {{2{Ni}} + k} \right)} \\{h_{21}\left( {{2{Ni}} + k} \right)} & {h_{22}\left( {{2{Ni}} + k} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + k} \right)} \\{s\; 2\left( {{2{Ni}} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 112}\end{matrix}$

Furthermore, for symbol number 2Ni+N−1:

Math 120

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N - 1} \right)} \\{r\; 2\left( {{2{Ni}} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2{Ni}} + N - 1} \right)} & {h_{12}\left( {{2{Ni}} + N - 1} \right)} \\{h_{21}\left( {{2{Ni}} + N - 1} \right)} & {h_{22}\left( {{2{Ni}} + N - 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N - 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N - 1} \right)} \\{s\; 2\left( {{2{Ni}} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 113}\end{matrix}$For symbol number 2Ni+N (where i is an integer greater than or equal tozero):Math 121

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N} \right)} \\{r\; 2\left( {{2{Ni}} + N} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2{Ni}} + N} \right)} & {h_{12}\left( {{2{Ni}} + N} \right)} \\{h_{21}\left( {{2{Ni}} + N} \right)} & {h_{22}\left( {{2{Ni}} + N} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N} \right)} \\{s\; 2\left( {{2{Ni}} + N} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 114}\end{matrix}$Here, j is an imaginary unit.For symbol number 2Ni+N+1:Math 122

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N + 1} \right)} \\{r\; 2\left( {{2{Ni}} + N + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2{Ni}} + N + 1} \right)} & {h_{12}\left( {{2{Ni}} + N + 1} \right)} \\{h_{21}\left( {{2{Ni}} + N + 1} \right)} & {h_{22}\left( {{2{Ni}} + N + 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N + 1})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N + 1} \right)} \\{s\; 2\left( {{2{Ni}} + N + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 115}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+N+k (k=0, 1, . . . , N−1):

Math 123

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N + k} \right)} \\{r\; 2\left( {{2{Ni}} + N + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2{Ni}} + N + k} \right)} & {h_{12}\left( {{2{Ni}} + N + k} \right)} \\{h_{21}\left( {{2{Ni}} + N + k} \right)} & {h_{22}\left( {{2{Ni}} + N + k} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N + k})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + k})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N + k} \right)} \\{s\; 2\left( {{2{Ni}} + N + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 116}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+2N−1:

Math 124

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + {2N} - 1} \right)} \\{r\; 2\left( {{2{Ni}} + {2N} - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2{Ni}} + {2N} - 1} \right)} & {h_{12}\left( {{2{Ni}} + {2N} - 1} \right)} \\{h_{21}\left( {{2{Ni}} + {2N} - 1} \right)} & {h_{22}\left( {{2{Ni}} + {2N} - 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + {2N} - 1})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + {2N} - 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + {2N} - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + {2N} - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + {2N} - 1} \right)} \\{s\; 2\left( {{2{Ni}} + {2N} - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 117}\end{matrix}$

In this case, it is assumed that only components of direct waves existin the channel elements h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t), that theamplitude components of the direct waves are all equal, and thatfluctuations do not occur over time. With these assumptions, Equations110-117 can be represented as follows.

For symbol number 2Ni (where i is an integer greater than or equal tozero):

Math 125

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {2{Ni}} \right)} \\{r\; 2\left( {2{Ni}} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{{A\;{\mathbb{e}}^{j0}}\;} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({2{Ni}})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({2{Ni}})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({2{Ni}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({2{Ni}})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {2{Ni}} \right)} \\{s\; 2\left( {2{Ni}} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 118}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+1:

Math 126

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + 1} \right)} \\{r\; 2\left( {{2{Ni}} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{{A\;{\mathbb{e}}^{j0}}\;} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + 1} \right)} \\{s\; 2\left( {{2{Ni}} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 119}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+k (k=0, 1, . . . , N−1):

Math 127

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + k} \right)} \\{r\; 2\left( {{2{Ni}} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{{A\;{\mathbb{e}}^{j0}}\;} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + k} \right)} \\{s\; 2\left( {{2{Ni}} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 120}\end{matrix}$

Furthermore, for symbol number 2Ni+N−1:

Math 128

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N - 1} \right)} \\{r\; 2\left( {{2{Ni}} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{{A\;{\mathbb{e}}^{j0}}\;} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N - 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N - 1} \right)} \\{s\; 2\left( {{2{Ni}} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 121}\end{matrix}$For symbol number 2Ni+N (where i is an integer greater than or equal tozero):Math 129

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N} \right)} \\{r\; 2\left( {{2{Ni}} + N} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{{A\;{\mathbb{e}}^{j0}}\;} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N} \right)} \\{s\; 2\left( {{2{Ni}} + N} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 122}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+N+1:

Math 130

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N + 1} \right)} \\{r\; 2\left( {{2{Ni}} + N + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{{A\;{\mathbb{e}}^{j0}}\;} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N + 1})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N + 1} \right)} \\{s\; 2\left( {{2{Ni}} + N + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 123}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+N+k (k=0, 1, . . . , N−1):

Math 131

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N + k} \right)} \\{r\; 2\left( {{2{Ni}} + N + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{{A\;{\mathbb{e}}^{j0}}\;} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N + k})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + k})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N + k} \right)} \\{s\; 2\left( {{2{Ni}} + N + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 124}\end{matrix}$

Furthermore, for symbol number 2Ni+2N−1:

Math 132

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + {2N} - 1} \right)} \\{r\; 2\left( {{2{Ni}} + {2N} - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{{A\;{\mathbb{e}}^{j0}}\;} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + {2N} - 1})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + {2N} - 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + {2N} - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + {2N} - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + {2N} - 1} \right)} \\{s\; 2\left( {{2{Ni}} + {2N} - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 125}\end{matrix}$

In Equations 118-125, let A be a real number and q be a complex number.Equations 118-125 can be represented as follows.

For symbol number 2Ni (where i is an integer greater than or equal tozero):

Math 133

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {2{Ni}} \right)} \\{r\; 2\left( {2{Ni}} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} \\{\mathbb{e}}^{j0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({2{Ni}})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({2{Ni}})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({2{Ni}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({2{Ni}})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {2{Ni}} \right)} \\{s\; 2\left( {2{Ni}} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 126}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+1:

Math 134

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + 1} \right)} \\{r\; 2\left( {{2{Ni}} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} \\{\mathbb{e}}^{j0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + 1} \right)} \\{s\; 2\left( {{2{Ni}} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 127}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+k (k=0, 1, . . . , N−1):

Math 135

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + k} \right)} \\{r\; 2\left( {{2{Ni}} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} \\{\mathbb{e}}^{j0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + k} \right)} \\{s\; 2\left( {{2{Ni}} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 128}\end{matrix}$

Furthermore, for symbol number 2Ni+N−1:

Math 136

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N - 1} \right)} \\{r\; 2\left( {{2{Ni}} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} \\{\mathbb{e}}^{j0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N - 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N - 1} \right)} \\{s\; 2\left( {{2{Ni}} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 129}\end{matrix}$For symbol number 2Ni+N (where i is an integer greater than or equal tozero):Math 137

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N} \right)} \\{r\; 2\left( {{2{Ni}} + N} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} \\{\mathbb{e}}^{j0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N} \right)} \\{s\; 2\left( {{2{Ni}} + N} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 130}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+N+1:

Math 138

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N + 1} \right)} \\{r\; 2\left( {{2{Ni}} + N + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} \\{\mathbb{e}}^{j0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N + 1})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N + 1} \right)} \\{s\; 2\left( {{2{Ni}} + N + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 131}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+N+k (k=0, 1, . . . , N−1):

Math 139

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + N + k} \right)} \\{r\; 2\left( {{2{Ni}} + N + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} \\{\mathbb{e}}^{j0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + N + k})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + k})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + N + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + N + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + N + k} \right)} \\{s\; 2\left( {{2{Ni}} + N + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 132}\end{matrix}$

Furthermore, for symbol number 2Ni+2N−1:

Math 140

$\begin{matrix}{\begin{pmatrix}{r\; 1\left( {{2{Ni}} + {2N} - 1} \right)} \\{r\; 2\left( {{2{Ni}} + {2N} - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} \\{\mathbb{e}}^{j0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2{Ni}} + {2N} - 1})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + {2N} - 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2{Ni}} + {2N} - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2{Ni}} + {2N} - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2{Ni}} + {2N} - 1} \right)} \\{s\; 2\left( {{2{Ni}} + {2N} - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 133}\end{matrix}$

As a result, when q is represented as follows, one of the signals s1 ands2 can no longer be obtained.

For symbol number 2Ni (where i is an integer greater than or equal tozero):

Math 141

$\begin{matrix}{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({2{Ni}})}} - {\theta_{21}{({2{Ni}})}}})}}}},{{- A}\;\beta\;{\mathbb{e}}^{j{({{\theta_{11}{({2{Ni}})}} - {\theta_{21}{({2{Ni}})}} - \delta})}}}} & {{Equation}\mspace{14mu} 134}\end{matrix}$

For symbol number 2Ni+1:

Math 142

$\begin{matrix}{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + 1})}} - {\theta_{21}{({{2{Ni}} + 1})}}})}}}},{{- A}\;{\beta\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + 1})}} - {\theta_{21}{({{2{Ni}} + 1})}} - \delta})}}}} & {{Equation}\mspace{14mu} 135}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+k (k=0, 1, . . . , N−1):

Math 143

$\begin{matrix}{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + k})}} - {\theta_{21}{({{2{Ni}} + k})}}})}}}},{{- A}\;\beta\;{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + k})}} - {\theta_{21}{({{2{Ni}} + k})}} - \delta})}}}} & {{Equation}\mspace{14mu} 136}\end{matrix}$

Furthermore, for symbol number 2Ni+N−1:

Math 144

$\begin{matrix}{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N - 1})}} - {\theta_{21}{({{2{Ni}} + N - 1})}}})}}}},{{- A}\;{\beta\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N - 1})}} - {\theta_{21}{({{2{Ni}} + N - 1})}} - \delta})}}}} & {{Equation}\mspace{14mu} 137}\end{matrix}$For symbol number 2Ni+N (where i is an integer greater than or equal tozero):Math 145

$\begin{matrix}{{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N})}} - {\theta_{21}{({{2{Ni}} + N})}}})}}}},{{- A}\;\alpha\;{\mathbb{e}}^{j{({{\theta_{11}{({{2N} + N})}} - {\theta_{21}{({{2{Ni}} + N})}} - \delta})}}}} & {{Equation}\mspace{14mu} 138}\end{matrix}$

For symbol number 2Ni+N+1:

Math 146

$\begin{matrix}{{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + 1})}} - {\theta_{21}{({{2{Ni}} + N + 1})}}})}}}},{{- A}\;{\alpha\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + 1})}} - {\theta_{21}{({{2{Ni}} + N + 1})}} - \delta})}}}} & {{Equation}\mspace{14mu} 139}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+N+k (k=0, 1, . . . , N−1):

Math 147

$\begin{matrix}{{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + k})}} - {\theta_{21}{({{2{Ni}} + N + k})}}})}}}},{{- A}\;\alpha\;{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + k})}} - {\theta_{21}{({{2{Ni}} + N + k})}} - \delta})}}}} & {{Equation}\mspace{14mu} 140}\end{matrix}$

Furthermore, for symbol number 2Ni+2N−1:

Math 148

$\begin{matrix}{{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + {2N} - 1})}} - {\theta_{21}{({{2{Ni}} + {2N} - 1})}}})}}}},{{- A}\;\alpha\;{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + {2N} - 1})}} - {\theta_{21}{({{2{Ni}} + {2N} - 1})}} - \delta})}}}} & {{Equation}\mspace{14mu} 141}\end{matrix}$

In this case, if q has the same solution in symbol numbers 2Ni through2Ni+N−1, then since the channel elements of the direct waves do notgreatly fluctuate, excellent reception quality can no longer be obtainedfor any of the symbol numbers. Therefore, it is difficult to achieve theability to correct errors, even if error correction codes areintroduced. Accordingly, for q not to have the same solution, Condition#7 or Condition #8 becomes necessary from Equations 134-141 and from thefact that α≠β when focusing on one of two solutions of q which does notinclude δ.

Math 149

Condition #7e ^(j(θ) ¹¹ ^((2Ni+x)−θ) ²¹ ^((2Ni+x))) ≠e ^(j(θ) ¹¹ ^((2Ni+y)−θ) ²¹^((2Ni+y))) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is, 0, 1, 2, . . . , N−2, N−1; andx≠y.)ande ^(j(θ) ¹¹ ^((2Ni+N+x)−θ) ²¹ ^((2Ni+N+x))) ≠e ^(j(θ) ¹¹ ^((2Ni+N+y)−θ)²¹ ^((2Ni+N+y))) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 150Condition #8e ^(j(θ) ¹¹ ^((2Ni+x)−θ) ²¹ ^((2Ni+x))) ≠e ^(j(θ) ¹¹ ^((2Ni+y)−θ) ²¹^((Ni+y))) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,2N−2,2N−1)

In this case, Condition #8 is similar to the conditions described inEmbodiment 1 through Embodiment 3. However, with regards to Condition#7, since α≠β, the solution not including δ among the two solutions of qis a different solution.

Next, design requirements for not only θ₁₁ and θ₁₂, but also for λ and δare described. It suffices to set λ to a certain value; it is thennecessary to establish requirements for δ. The following describes thedesign scheme for δ when λ is set to zero radians.

In this case, similar to the scheme of changing the precoding weights ina four-slot period (cycle), by defining δ so that π/2 radians≦|δ|≦πradians, excellent reception quality is achieved, particularly in an LOSenvironment.

In symbol numbers 2Ni through 2Ni+2N−1, two points q exist wherereception quality becomes poor, and therefore 4N such points exist. Inan LOS environment, in order to achieve excellent characteristics, these4N points should each have a different solution. In this case, focusingon amplitude, the following condition is necessary for Condition #7 orCondition #8, since α≠β.

Math 151

$\begin{matrix}{\alpha \neq \frac{1}{\beta}} & {{Condition}\mspace{14mu}{\# 9}}\end{matrix}$

As described above, when a transmission device transmits a plurality ofmodulated signals from a plurality of antennas in a MIMO system, theadvantageous effect of improved transmission quality, as compared toconventional spatial multiplexing MIMO system, is achieved in an LOSenvironment in which direct waves dominate by hopping between precodingweights regularly over time.

In the present embodiment, the structure of the reception device is asdescribed in Embodiment 1, and in particular with regards to thestructure of the reception device, operations have been described for alimited number of antennas, but the present invention may be embodied inthe same way even if the number of antennas increases. In other words,the number of antennas in the reception device does not affect theoperations or advantageous effects of the present embodiment.Furthermore, in the present embodiment, similar to Embodiment 1, theerror correction codes are not limited.

In the present embodiment, in contrast with Embodiment 1, the scheme ofchanging the precoding weights in the time domain has been described. Asdescribed in Embodiment 1, however, the present invention may besimilarly embodied by changing the precoding weights by using amulti-carrier transmission scheme and arranging symbols in the frequencydomain and the frequency-time domain. Furthermore, in the presentembodiment, symbols other than data symbols, such as pilot symbols(preamble, unique word, and the like), symbols for control information,and the like, may be arranged in the frame in any way.

Embodiment 5

In Embodiment 1 through Embodiment 4, the scheme of regularly hoppingbetween precoding weights has been described. In the present embodiment,a modification of this scheme is described.

In Embodiment 1 through Embodiment 4, the scheme of regularly hoppingbetween precoding weights as in FIG. 6 has been described. In thepresent embodiment, a scheme of regularly hopping between precodingweights that differs from FIG. 6 is described.

As in FIG. 6, this scheme hops between four different precoding weights(matrices). FIG. 22 shows the hopping scheme that differs from FIG. 6.In FIG. 22, four different precoding weights (matrices) are representedas W1, W2, W3, and W4. (For example, W1 is the precoding weight (matrix)in Equation 37, W2 is the precoding weight (matrix) in Equation 38, W3is the precoding weight (matrix) in Equation 39, and W4 is the precodingweight (matrix) in Equation 40.) In FIG. 3, elements that operate in asimilar way to FIG. 3 and FIG. 6 bear the same reference signs.

The parts unique to FIG. 22 are as follows.

The first period (cycle) 2201, the second period (cycle) 2202, the thirdperiod (cycle) 2203, . . . are all four-slot period (cycle)s.

A different precoding weight matrix is used in each of the four slots,i.e. W1, W2, W3, and W4 are each used once.

It is not necessary for W1, W2, W3, and W4 to be in the same order inthe first period (cycle) 2201, the second period (cycle) 2202, the thirdperiod (cycle) 2203, . . . .

In order to implement this scheme, a precoding weight generating unit2200 receives, as an input, a signal regarding a weighting scheme andoutputs information 2210 regarding precoding weights in order for eachperiod (cycle). The weighting unit 600 receives, as inputs, thisinformation, s1(t), and s2(t), performs weighting, and outputs z1(t) andz2(t).

FIG. 23 shows a different weighting scheme than FIG. 22 for the aboveprecoding scheme. In FIG. 23, the difference from FIG. 22 is that asimilar scheme to FIG. 22 is achieved by providing a reordering unitafter the weighting unit and by reordering signals.

In FIG. 23, the precoding weight generating unit 2200 receives, as aninput, information 315 regarding a weighting scheme and outputsinformation 2210 on precoding weights in the order of precoding weightsW1, W2, W3, W4, W1, W2, W3, W4, . . . . Accordingly, the weighting unit600 uses the precoding weights in the order of precoding weights W1, W2,W3, W4, W1, W2, W3, W4, . . . and outputs precoded signals 2300A and2300B.

A reordering unit 2300 receives, as inputs, the precoded signals 2300Aand 2300B, reorders the precoded signals 2300A and 2300B in the order ofthe first period (cycle) 2201, the second period (cycle) 2202, and thethird period (cycle) 2203 in FIG. 23, and outputs z1(t) and z2(t).

Note that in the above description, the period (cycle) for hoppingbetween precoding weights has been described as having four slots forthe sake of comparison with FIG. 6. As in Embodiment 1 throughEmbodiment 4, however, the present invention may be similarly embodiedwith a period (cycle) having other than four slots.

Furthermore, in Embodiment 1 through Embodiment 4, and in the aboveprecoding scheme, within the period (cycle), the value of δ and β hasbeen described as being the same for each slot, but the value of δ and βmay change in each slot.

As described above, when a transmission device transmits a plurality ofmodulated signals from a plurality of antennas in a MIMO system, theadvantageous effect of improved transmission quality, as compared toconventional spatial multiplexing MIMO system, is achieved in an LOSenvironment in which direct waves dominate by hopping between precodingweights regularly over time.

In the present embodiment, the structure of the reception device is asdescribed in Embodiment 1, and in particular with regards to thestructure of the reception device, operations have been described for alimited number of antennas, but the present invention may be embodied inthe same way even if the number of antennas increases. In other words,the number of antennas in the reception device does not affect theoperations or advantageous effects of the present embodiment.Furthermore, in the present embodiment, similar to Embodiment 1, theerror correction codes are not limited.

In the present embodiment, in contrast with Embodiment 1, the scheme ofchanging the precoding weights in the time domain has been described. Asdescribed in Embodiment 1, however, the present invention may besimilarly embodied by changing the precoding weights by using amulti-carrier transmission scheme and arranging symbols in the frequencydomain and the frequency-time domain. Furthermore, in the presentembodiment, symbols other than data symbols, such as pilot symbols(preamble, unique word, and the like), symbols for control information,and the like, may be arranged in the frame in any way.

Embodiment 6

In Embodiments 1-4, a scheme for regularly hopping between precodingweights has been described. In the present embodiment, a scheme forregularly hopping between precoding weights is again described,including the content that has been described in Embodiments 1-4.

First, out of consideration of an LOS environment, a scheme of designinga precoding matrix is described for a 2×2 spatial multiplexing MIMOsystem that adopts precoding in which feedback from a communicationpartner is not available.

FIG. 30 shows a model of a 2×2 spatial multiplexing MIMO system thatadopts precoding in which feedback from a communication partner is notavailable.

An information vector z is encoded and interleaved. As output of theinterleaving, an encoded bit vector u(p)=(u₁(p), u₂(p)) is acquired(where p is the slot time). Let u_(i)(p)=(u_(i1)(p), . . . , u_(ih)(p))(where h is the number of transmission bits per symbol). Letting asignal after modulation (mapping) be s(p)=(s1(p), s2(p))^(T) and aprecoding matrix be F(p), a precoded symbol x(p)=(x₁(p), x₂(p))^(T) isrepresented by the following equation.

Math 152

$\begin{matrix}\begin{matrix}{{x(p)} = \left( {{x_{1}(p)},{x_{2}(p)}} \right)^{T}} \\{= {{F(p)}{s(p)}}}\end{matrix} & {{Equation}\mspace{14mu} 142}\end{matrix}$

Accordingly, letting a received vector be y(p)=(y₁(p), y₂(p))^(T), thereceived vector y(p) is represented by the following equation.

Math 153

$\begin{matrix}\begin{matrix}{{y(p)} = \left( {{y_{1}(p)},{y_{2}(p)}} \right)^{T}} \\{= {{{H(p)}{F(p)}{s(p)}} + {n(p)}}}\end{matrix} & {{Equation}\mspace{14mu} 143}\end{matrix}$

In this Equation, H(p) is the channel matrix, n(p)=(n₁(p), n₂(p))^(T) isthe noise vector, and n_(i)(p) is the i.i.d. complex Gaussian randomnoise with an average value 0 and variance σ². Letting the Rician factorbe K, the above equation can be represented as follows.

Math 154

$\begin{matrix}\begin{matrix}{{y(p)} = \left( {{y_{1}(p)},{y_{2}(p)}} \right)^{T}} \\{= {{\left( {{\sqrt{\frac{K}{K + 1}}{H_{d}(p)}} + {\sqrt{\frac{1}{K + 1}}{H_{s}(p)}}} \right){F(p)}{s(p)}} + {n(p)}}}\end{matrix} & {{Equation}\mspace{14mu} 144}\end{matrix}$

In this equation, H_(d)(p) is the channel matrix for the direct wavecomponents, and H_(s)(p) is the channel matrix for the scattered wavecomponents. Accordingly, the channel matrix H(p) is represented asfollows.

Math 155

$\begin{matrix}\begin{matrix}{{H(p)} = {{\sqrt{\frac{K}{K + 1}}{H_{d}(p)}} + {\sqrt{\frac{1}{K + 1}}{H_{s}(p)}}}} \\{= {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}h_{11,d} & h_{12,d} \\h_{21,d} & h_{22,d}\end{pmatrix}} +}} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(p)} & {h_{12,s}(p)} \\{h_{21,s}(p)} & {h_{22,s}(p)}\end{pmatrix}}\end{matrix} & {{Equation}\mspace{14mu} 145}\end{matrix}$

In Equation 145, it is assumed that the direct wave environment isuniquely determined by the positional relationship between transmitters,and that the channel matrix H_(d)(p) for the direct wave components doesnot fluctuate with time. Furthermore, in the channel matrix H_(d)(p) forthe direct wave components, it is assumed that as compared to theinterval between transmitting antennas, the probability of anenvironment with a sufficiently long distance between transmission andreception devices is high, and therefore that the channel matrix for thedirect wave components can be treated as a non-singular matrix.Accordingly, the channel matrix H_(d)(p) is represented as follows.

Math 156

$\begin{matrix}\begin{matrix}{{H_{d}(p)} = \begin{pmatrix}h_{11,d} & h_{12,d} \\h_{21,d} & h_{22,d}\end{pmatrix}} \\{= \begin{pmatrix}{A\;{\mathbb{e}}^{j\psi}} & q \\{A\;{\mathbb{e}}^{j\psi}} & q\end{pmatrix}}\end{matrix} & {{Equation}\mspace{14mu} 146}\end{matrix}$

In this equation, let A be a positive real number and q be a complexnumber. Subsequently, out of consideration of an LOS environment, ascheme of designing a precoding matrix is described for a 2×2 spatialmultiplexing MIMO system that adopts precoding in which feedback from acommunication partner is not available.

From Equations 144 and 145, it is difficult to seek a precoding matrixwithout appropriate feedback in conditions including scattered waves,since it is difficult to perform analysis under conditions includingscattered waves. Additionally, in a NLOS environment, little degradationin reception quality of data occurs as compared to an LOS environment.Therefore, the following describes a scheme of designing precodingmatrices without appropriate feedback in an LOS environment (precodingmatrices for a precoding scheme that hops between precoding matricesover time).

As described above, since it is difficult to perform analysis underconditions including scattered waves, an appropriate precoding matrixfor a channel matrix including components of only direct waves is soughtfrom Equations 144 and 145. Therefore, in Equation 144, the case whenthe channel matrix includes components of only direct waves isconsidered. It follows that from Equation 146, Equation 144 can berepresented as follows.

Math 157

$\begin{matrix}\begin{matrix}{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{{H_{d}(p)}{F(p)}{s(p)}} + {n(p)}}} \\{= {{\begin{pmatrix}{A\;{\mathbb{e}}^{j\psi}} & q \\{A\;{\mathbb{e}}^{j\psi}} & q\end{pmatrix}{F(p)}{s(p)}} + {n(p)}}}\end{matrix} & {{Equation}\mspace{14mu} 147}\end{matrix}$

In this equation, a unitary matrix is used as the precoding matrix.Accordingly, the precoding matrix is represented as follows.

Math 158

$\begin{matrix}{{F(p)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 148}\end{matrix}$

In this equation, λ is a fixed value. Therefore, Equation 147 can berepresented as follows.

Math 159

$\begin{matrix}{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\psi}} & q \\{A\;{\mathbb{e}}^{j\psi}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}}} & {{Equation}\mspace{14mu} 149}\end{matrix}$

As is clear from Equation 149, when the reception device performs linearoperation of Zero Forcing (ZF) or the Minimum Mean Squared Error (MMSE),the transmitted bit cannot be determined by s1(p), s2(p). Therefore, theiterative APP (or iterative Max-log APP) or APP (or Max-log APP)described in Embodiment 1 is performed (hereafter referred to as MaximumLikelihood (ML) calculation), the log-likelihood ratio of each bittransmitted in s1(p), s2(p) is sought, and decoding with errorcorrection codes is performed. Accordingly, the following describes ascheme of designing a precoding matrix without appropriate feedback inan LOS environment for a reception device that performs ML calculation.

The precoding in Equation 149 is considered. The right-hand side andleft-hand side of the first line are multiplied by e^(−jΨ), andsimilarly the right-hand side and left-hand side of the second line aremultiplied by e^(−jΨ). The following equation represents the result.

Math 160

$\begin{matrix}\begin{matrix}{\begin{pmatrix}{{\mathbb{e}}^{- {j\psi}}{y_{1}(p)}} \\{{\mathbb{e}}^{- {j\psi}}{y_{2}(p)}}\end{pmatrix} = {{\mathbb{e}}^{- {j\psi}}\left\{ {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\psi}} & q \\{A\;{\mathbb{e}}^{j\psi}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}} \right\}}} \\{= {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & {{\mathbb{e}}^{- {j\psi}}q} \\{A\;{\mathbb{e}}^{j0}} & {{\mathbb{e}}^{- {j\psi}}q}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {{\mathbb{e}}^{- {j\psi}}{n(p)}}}}\end{matrix} & {{Equation}\mspace{14mu} 150}\end{matrix}$

e^(−jΨ)y₁(p), e^(−jΨ)y₂(p), and e^(−jΨ)q are respectively redefined asy₁(p), y₂(p), and q. Furthermore, since e^(−jΨ)n(p)=(e^(−jΨ)n₁(p),e^(−jΨ)n₂(p))^(T), and e^(−jΨ)n₁(p), e^(−jΨ)n₂(p) are the independentidentically distributed (i.i.d.) complex Gaussian random noise with anaverage value 0 and variance σ², e^(−jΨ)n(p) is redefined as n(p). As aresult, generality is not lost by restating Equation 150 as Equation151.

Math 161

$\begin{matrix}{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & q \\{A\;{\mathbb{e}}^{j0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}}} & {{Equation}\mspace{14mu} 151}\end{matrix}$

Next, Equation 151 is transformed into Equation 152 for the sake ofclarity.

Math 162

$\begin{matrix}{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} \\{\mathbb{e}}^{j0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}}} & {{Equation}\mspace{14mu} 152}\end{matrix}$

In this case, letting the minimum Euclidian distance between a receivedsignal point and a received candidate signal point be d_(min) ², then apoor point has a minimum value of zero for d_(min) ², and two values ofq exist at which conditions are poor in that all of the bits transmittedby s1(p) and all of the bits transmitted by s2(p) being eliminated.

In Equation 152, when s1(p) does not exist.

Math 163

$\begin{matrix}{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{(p)}} - {\theta_{21}{(p)}}})}}}} & {{Equation}\mspace{14mu} 153}\end{matrix}$

In Equation 152, when s2(p) does not exist.

Math 164q=−Aα _(e) ^(j(θ) ¹¹ ^((p)−θ) ²¹ ^((p)−π))  Equation 154

(Hereinafter, the values of q satisfying Equations 153 and 154 arerespectively referred to as “poor reception points for s1 and s2”).

When Equation 153 is satisfied, since all of the bits transmitted bys1(p) are eliminated, the received log-likelihood ratio cannot be soughtfor any of the bits transmitted by s1(p). When Equation 154 issatisfied, since all of the bits transmitted by s2(p) are eliminated,the received log-likelihood ratio cannot be sought for any of the bitstransmitted by s2(p).

A broadcast/multicast transmission system that does not change theprecoding matrix is now considered. In this case, a system model isconsidered in which a base station transmits modulated signals using aprecoding scheme that does not hop between precoding matrices, and aplurality of terminals (F terminals) receive the modulated signalstransmitted by the base station.

It is considered that the conditions of direct waves between the basestation and the terminals change little over time. Therefore, fromEquations 153 and 154, for a terminal that is in a position fitting theconditions of Equation 155 or Equation 156 and that is in an LOSenvironment where the Rician factor is large, the possibility ofdegradation in the reception quality of data exists. Accordingly, toresolve this problem, it is necessary to change the precoding matrixover time.

Math 165

$\begin{matrix}{q \approx {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{(p)}} - {\theta_{21}{(p)}}})}}}} & {{Equation}\mspace{14mu} 155}\end{matrix}$Math 166q≈−Aα _(e) ^(j(θ) ¹¹ ^((p)−θ) ²¹ ^((p)−π))  Equation 156

A scheme of regularly hopping between precoding matrices over a timeperiod (cycle) with N slots (hereinafter referred to as a precodinghopping scheme) is considered.

Since there are N slots in the time period (cycle), N varieties ofprecoding matrices F[i] based on Equation 148 are prepared (i=0, 1, . .. , N−1). In this case, the precoding matrices F[i] are represented asfollows.

Math 167

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{\lbrack i\rbrack}}}} & {\mathbb{e}}^{j{({{\theta_{21}{\lbrack i\rbrack}} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 157}\end{matrix}$

In this equation, let a not change over time, and let λ also not changeover time (though change over time may be allowed).

As in Embodiment 1, F[i] is the precoding matrix used to obtain aprecoded signal x (p=N×k+i) in Equation 142 for time N×k+i (where k isan integer equal to or greater than 0, and i=0, 1, . . . , N−1). Thesame is true below as well.

At this point, based on Equations 153 and 154, design conditions such asthe following are important for the precoding matrices for precodinghopping.

Math 168

Condition #10e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x])) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹ ^([y])) for∀x,∀y(x≠y;x,y=0,1, . . . ,N−1)  Equation 158Math 169Condition #11e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x]−π)) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹ ^([y]−π)) for∀x,∀y(x≠y;x,y=0,1, . . . ,N−1)  Equation 159

From Condition #10, in all of the Γ terminals, there is one slot or lesshaving poor reception points for s1 among the N slots in a time period(cycle). Accordingly, the log-likelihood ratio for bits transmitted bys1(p) can be obtained for at least N−1 slots. Similarly, from Condition#11, in all of the Γ terminals, there is one slot or less having poorreception points for s2 among the N slots in a time period (cycle).Accordingly, the log-likelihood ratio for bits transmitted by s2(p) canbe obtained for at least N−1 slots.

In this way, by providing the precoding matrix design model of Condition#10 and Condition #11, the number of bits for which the log-likelihoodratio is obtained among the bits transmitted by s1(p), and the number ofbits for which the log-likelihood ratio is obtained among the bitstransmitted by s2(p) is guaranteed to be equal to or greater than afixed number in all of the Γ terminals. Therefore, in all of the Γterminals, it is considered that degradation of data reception qualityis moderated in an LOS environment where the Rician factor is large.

The following shows an example of a precoding matrix in the precodinghopping scheme.

The probability density distribution of the phase of a direct wave canbe considered to be evenly distributed over [0 2π]. Therefore, theprobability density distribution of the phase of q in Equations 151 and152 can also be considered to be evenly distributed over [0 2π].Accordingly, the following is established as a condition for providingfair data reception quality insofar as possible for Γ terminals in thesame LOS environment in which only the phase of q differs.

Condition #12

When using a precoding hopping scheme with an N-slot time period(cycle), among the N slots in the time period (cycle), the poorreception points for s1 are arranged to have an even distribution interms of phase, and the poor reception points for s2 are arranged tohave an even distribution in terms of phase.

The following describes an example of a precoding matrix in theprecoding hopping scheme based on Condition #10 through Condition #12.Let α=1.0 in the precoding matrix in Equation 157.

Example #5

Let the number of slots N in the time period (cycle) be 8. In order tosatisfy Condition #10 through Condition #12, precoding matrices for aprecoding hopping scheme with an N=8 time period (cycle) are provided asin the following equation.

Math 170

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 160}\end{matrix}$

Here, j is an imaginary unit, and i=0, 1, . . . , 7. Instead of Equation160, Equation 161 may be provided (where λ and θ₁₁[i] do not change overtime (though change may be allowed)).

Math 171

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 161}\end{matrix}$

Accordingly, the poor reception points for s1 and s2 become as in FIGS.31A and 31B. (In FIGS. 31A and 31B, the horizontal axis is the realaxis, and the vertical axis is the imaginary axis.) Instead of Equations160 and 161, Equations 162 and 163 may be provided (where i=0, 1, . . ., 7, and where λ and θ₁₁[i] do not change over time (though change maybe allowed)).

Math 172

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 162}\end{matrix}$Math 173

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 163}\end{matrix}$

Next, the following is established as a condition, different fromCondition #12, for providing fair data reception quality insofar aspossible for Γ terminals in the same LOS environment in which only thephase of q differs.

Condition #13

When using a precoding hopping scheme with an N-slot time period(cycle), in addition to the condition

Math 174e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x])) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹ ^([y]−π)) for∀x,∀y(x,y=0,1, . . . ,N−1)  Equation 164the poor reception points for s1 and the poor reception points for s2are arranged to be in an even distribution with respect to phase in theN slots in the time period (cycle).

The following describes an example of a precoding matrix in theprecoding hopping scheme based on Condition #10, Condition #11, andCondition #13. Let α=1.0 in the precoding matrix in Equation 157.

Example #6

Let the number of slots N in the time period (cycle) be 4. Precodingmatrices for a precoding hopping scheme with an N=4 time period (cycle)are provided as in the following equation.

Math 175

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 165}\end{matrix}$

Here, j is an imaginary unit, and i=0, 1, 2, 3. Instead of Equation 165,Equation 166 may be provided (where λ and θ₁₁[i] do not change over time(though change may be allowed)).

Math 176

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 166}\end{matrix}$

Accordingly, the poor reception points for s1 and s2 become as in FIG.32. (In FIG. 32, the horizontal axis is the real axis, and the verticalaxis is the imaginary axis.) Instead of Equations 165 and 166, Equations167 and 168 may be provided (where i=0, 1, 2, 3, and where λ and θ₁₁[i]do not change over time (though change may be allowed)).

Math 177

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 167}\end{matrix}$Math 178

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 168}\end{matrix}$

Next, a precoding hopping scheme using a non-unitary matrix isdescribed.

Based on Equation 148, the precoding matrices presently underconsideration are represented as follows.

Math 179

$\begin{matrix}{{F(p)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{(p)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{(p)}}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 169}\end{matrix}$

Equations corresponding to Equations 151 and 152 are represented asfollows.

Math 180

$\begin{matrix}{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{(p)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{(p)}}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}}} & {{Equation}\mspace{14mu} 170}\end{matrix}$Math 181

$\begin{matrix}{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{(p)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{(p)}}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}}} & {{Equation}\mspace{14mu} 171}\end{matrix}$

In this case, there are two q at which the minimum value d_(min) ² ofthe Euclidian distance between a received signal point and a receivedcandidate signal point is zero.

In Equation 171, when s1(p) does not exist:

Math 182

$\begin{matrix}{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{(p)}} - {\theta_{21}{(p)}}})}}}} & {{Equation}\mspace{14mu} 172}\end{matrix}$

In Equation 171, when s2(p) does not exist:

Math 183q=−Aα _(e) ^(j(θ) ¹¹ ^((p)−θ) ²¹ ^((p)−δ))  Equation 173

In the precoding hopping scheme for an N-slot time period (cycle), byreferring to Equation 169, N varieties of the precoding matrix F[i] arerepresented as follows.

Math 184

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{\lbrack i\rbrack}}}} & {\mathbb{e}}^{j{({{\theta_{21}{\lbrack i\rbrack}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 174}\end{matrix}$

In this equation, let α and δ not change over time. At this point, basedon Equations 34 and 35, design conditions such as the following areprovided for the precoding matrices for precoding hopping.

Math 185

Condition #14e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x])) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹ ^([y])) for∀x,∀y(x≠y;x,y=0,1, . . . ,N−1)  Equation 175Math 186Condition #15e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x]−δ)) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹ ^([y]−δ)) for∀x,∀y(x≠y;x,y=0,1, . . . ,N−1)  Equation 176

Example #7

Let α=1.0 in the precoding matrix in Equation 174. Let the number ofslots N in the time period (cycle) be 16. In order to satisfy Condition#12, Condition #14, and Condition #15, precoding matrices for aprecoding hopping scheme with an N=16 time period (cycle) are providedas in the following equations.

For i=0, 1, . . . , 7:

Math 187

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 177}\end{matrix}$For i=8, 9, . . . , 15:Math 188

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{7\;\pi}{8}})}} \\{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0}\end{pmatrix}}} & {{Equation}\mspace{14mu} 178}\end{matrix}$

Furthermore, a precoding matrix that differs from Equations 177 and 178can be provided as follows.

For i=0, 1, . . . , 7:

Math 189

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 179}\end{matrix}$

For i=8, 9, . . . , 15:

Math 190

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\;\pi}{8}})}} \\{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 180}\end{matrix}$

Accordingly, the poor reception points for s1 and s2 become as in FIGS.33A and 33B.

(In FIGS. 33A and 33B, the horizontal axis is the real axis, and thevertical axis is the imaginary axis.) Instead of Equations 177 and 178,and Equations 179 and 180, precoding matrices may be provided as below.

For i=0, 1, . . . , 7:

Math 191

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 181}\end{matrix}$For i=8, 9, . . . , 15:Math 192

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} + \frac{7\;\pi}{8}})}} \\{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0}\end{pmatrix}}} & {{Equation}\mspace{14mu} 182}\end{matrix}$

or

For i=0, 1, . . . , 7:

Math 193

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 183}\end{matrix}$For i=8, 9, . . . , 15:Math 194

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\;\pi}{8}})}} \\{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 184}\end{matrix}$(In Equations 177-184, 7π/8 may be changed to −7π/8.) Next, thefollowing is established as a condition, different from Condition #12,for providing fair data reception quality insofar as possible for Γterminals in the same LOS environment in which only the phase of qdiffers.Condition #16

When using a precoding hopping scheme with an N-slot time period(cycle), the following condition is set:

Math 195e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x])) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹ ^([y]−δ)) for∀x,∀y(x,y=0,1, . . . ,N−1)  Equation 185

and the poor reception points for s1 and the poor reception points fors2 are arranged to be in an even distribution with respect to phase inthe N slots in the time period (cycle).

The following describes an example of a precoding matrix in theprecoding hopping scheme based on Condition #14, Condition #15, andCondition #16. Let α=1.0 in the precoding matrix in Equation 174.

Example #8

Let the number of slots N in the time period (cycle) be 8. Precodingmatrices for a precoding hopping scheme with an N=8 time period (cycle)are provided as in the following equation.

Math 196

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 186}\end{matrix}$

Here, i=0, 1, . . . , 7.

Furthermore, a precoding matrix that differs from Equation 186 can beprovided as follows (where i=0, 1, . . . , 7, and where λ and θ₁₁[i] donot change over time (though change may be allowed)).

Math 197

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 187}\end{matrix}$

Accordingly, the poor reception points for s1 and s2 become as in FIG.34. Instead of Equations 186 and 187, precoding matrices may be providedas follows (where i=0, 1, . . . , 7, and where λ and θ₁₁[i] do notchange over time (though change may be allowed)).

Math 198

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 188}\end{matrix}$

or

Math 199

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 189}\end{matrix}$(In Equations 186-189, 7π/8 may be changed to −7π/8.)

Next, in the precoding matrix of Equation 174, a precoding hoppingscheme that differs from Example #7 and Example #8 by letting α≠1, andby taking into consideration the distance in the complex plane betweenpoor reception points, is examined.

In this case, the precoding hopping scheme for an N-slot time period(cycle) of Equation 174 is used, and from Condition #14, in all of the Γterminals, there is one slot or less having poor reception points for s1among the N slots in a time period (cycle). Accordingly, thelog-likelihood ratio for bits transmitted by s1(p) can be obtained forat least N−1 slots. Similarly, from Condition #15, in all of the Fterminals, there is one slot or less having poor reception points for s2among the N slots in a time period (cycle). Accordingly, thelog-likelihood ratio for bits transmitted by s2(p) can be obtained forat least N−1 slots.

Therefore, it is clear that a larger value for N in the N-slot timeperiod (cycle) increases the number of slots in which the log-likelihoodratio can be obtained.

Incidentally, since the influence of scattered wave components is alsopresent in an actual channel model, it is considered that when thenumber of slots N in the time period (cycle) is fixed, there is apossibility of improved data reception quality if the minimum distancein the complex plane between poor reception points is as large aspossible. Accordingly, in the context of Example #7 and Example #8,precoding hopping schemes in which α≠1 and which improve on Example #7and Example #8 are considered. The precoding scheme that improves onExample #8 is easier to understand and is therefore described first.

Example #9

From Equation 186, the precoding matrices in an N=8 time period (cycle)precoding hopping scheme that improves on Example #8 are provided in thefollowing equation.

Math 200

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 190}\end{matrix}$

Here, i=0, 1, . . . , 7. Furthermore, precoding matrices that differfrom Equation 190 can be provided as follows (where i=0, 1, . . . , 7,and where λ and θ₁₁[i] do not change over time (though change may beallowed)).

Math 201

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 191}\end{matrix}$

or

Math 202

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 192}\end{matrix}$

or

Math 203

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 193}\end{matrix}$

or

Math 204

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} - \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 194}\end{matrix}$

or

Math 205

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda - \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 195}\end{matrix}$

or

Math 206

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} - \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 196}\end{matrix}$

or

Math 207

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda - \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 197}\end{matrix}$

Therefore, the poor reception points for s1 and s2 are represented as inFIG. 35A when α<1.0 and as in FIG. 35B when α>1.0.

-   -   (i) When α<1.0

When α<1.0, the minimum distance in the complex plane between poorreception points is represented as min{d_(#1,#2), d_(#1,#3)} whenfocusing on the distance (d_(#1,#2)) between poor reception points #1and #2 and the distance (d_(#1,#3)) between poor reception points #1 and#3. In this case, the relationship between α and d_(#1,#2) and between αand d_(#1,#3) is shown in FIG. 36. The α which makes min{d_(#1,#2),d_(#1,#3)} the largest is as follows.

Math 208

$\begin{matrix}\begin{matrix}{\alpha = \frac{1}{\sqrt{{\cos\left( \frac{\pi}{8} \right)} + {\sqrt{3}{\sin\left( \frac{\pi}{8} \right)}}}}} \\{\approx 0.7938}\end{matrix} & {{Equation}\mspace{14mu} 198}\end{matrix}$

The min{d_(#1,#2), d_(#1,#3)} in this case is as follows.

Math 209

$\begin{matrix}\begin{matrix}{{\min\left\{ {d_{{\# 1},{\# 2}},d_{{\# 1},{\# 3}}} \right\}} = \frac{2A\;{\sin\left( \frac{\pi}{8} \right)}}{\sqrt{{\cos\left( \frac{\pi}{8} \right)} + {\sqrt{3}{\sin\left( \frac{\pi}{8} \right)}}}}} \\{\approx {0.6076A}}\end{matrix} & {{Equation}\mspace{14mu} 199}\end{matrix}$

Therefore, the precoding scheme using the value of α in Equation 198 forEquations 190-197 is effective. Setting the value of α as in Equation198 is one appropriate scheme for obtaining excellent data receptionquality. Setting α to be a value near Equation 198, however, maysimilarly allow for excellent data reception quality. Accordingly, thevalue to which α is set is not limited to Equation 198.

(ii) When α>1.0

When α>1.0, the minimum distance in the complex plane between poorreception points is represented as min{d_(#4,#5), d_(#4,#6)} whenfocusing on the distance (d_(#4,#5)) between poor reception points #4and #5 and the distance (d_(#4,#6)) between poor reception points #4 and#6. In this case, the relationship between α and d_(#4,#5) and between αand d_(#4,#6) is shown in FIG. 37. The α which makes min{d_(#4,#5),d_(#4,#6)} the largest is as follows.

Math 210

$\begin{matrix}\begin{matrix}{\alpha = \sqrt{{\cos\left( \frac{\pi}{8} \right)} + {\sqrt{3}{\sin\left( \frac{\pi}{8} \right)}}}} \\{\approx 1.2596}\end{matrix} & {{Equation}\mspace{14mu} 200}\end{matrix}$

The min{d_(#4,#5), d_(#4,#6)} in this case is as follows.

Math 211

$\begin{matrix}\begin{matrix}{{\min\left\{ {d_{{\# 4},{\# 5}},d_{{\# 4},{\# 6}}} \right\}} = \frac{2A\;{\sin\left( \frac{\pi}{8} \right)}}{\sqrt{{\cos\left( \frac{\pi}{8} \right)} + {\sqrt{3}{\sin\left( \frac{\pi}{8} \right)}}}}} \\{\approx {0.6076A}}\end{matrix} & {{Equation}\mspace{14mu} 201}\end{matrix}$

Therefore, the precoding scheme using the value of α in Equation 200 forEquations 190-197 is effective. Setting the value of α as in Equation200 is one appropriate scheme for obtaining excellent data receptionquality. Setting α to be a value near Equation 200, however, maysimilarly allow for excellent data reception quality. Accordingly, thevalue to which α is set is not limited to Equation 200.

Example #10

Based on consideration of Example #9, the precoding matrices in an N=16time period (cycle) precoding hopping scheme that improves on Example #7are provided in the following equations (where λ and θ₁₁[i] do notchange over time (though change may be allowed)).

For i=0, 1, . . . , 7:

Math 212

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 202}\end{matrix}$For i=8, 9, . . . , 15:Math 213

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 203}\end{matrix}$

or

For i=0, 1, . . . , 7:

Math 214

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack i\rbrack}} & {\alpha \times {\mathbb{e}}^{j\;{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 204}\end{matrix}$For i=8, 9, . . . , 15:Math 215

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{{j\theta}_{11}{\lbrack i\rbrack}} & {\alpha \times {\mathbb{e}}^{j\;{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 205}\end{matrix}$

or

For i=0, 1, . . . , 7:

Math 216

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({- \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 206}\end{matrix}$

For i=8, 9, . . . , 15:

Math 217

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({- \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 207}\end{matrix}$

or

For i=0, 1, . . . , 7:

Math 218

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack i\rbrack}} & {\alpha \times {\mathbb{e}}^{j\;{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 208}\end{matrix}$For i=8, 9, . . . , 15:Math 219

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{{j\theta}_{11}{\lbrack i\rbrack}} & {\alpha \times {\mathbb{e}}^{j\;{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 209}\end{matrix}$

or

For i=0, 1, . . . , 7:

Math 220

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} - \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 210}\end{matrix}$For i=8, 9, . . . , 15:Math 221

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} - \frac{7\pi}{8}})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 211}\end{matrix}$

or

For i=0, 1, . . . , 7:

Math 222

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack i\rbrack}} & {\alpha \times {\mathbb{e}}^{j\;{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda - \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 212}\end{matrix}$

For i=8, 9, . . . , 15:

Math 223

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda - \frac{7\;\pi}{8}})}} \\{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 213}\end{matrix}$

or

For i=0, 1, . . . , 7:

Math 224

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} - \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 214}\end{matrix}$For i=8, 9, . . . , 15:Math 225

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} - \frac{7\;\pi}{8}})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 215}\end{matrix}$

or

For i=0, 1, . . . , 7:

Math 226

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda - \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 216}\end{matrix}$For i=8, 9, . . . , 15:Math 227

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda - \frac{7\;\pi}{8}})}} \\{\mathbb{e}}^{j\;{\theta_{11}{\lbrack i\rbrack}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 217}\end{matrix}$

The value of α in Equation 198 and in Equation 200 is appropriate forobtaining excellent data reception quality. The poor reception pointsfor s1 are represented as in FIGS. 38A and 38B when α<1.0 and as inFIGS. 39A and 39B when α>1.0.

In the present embodiment, the scheme of structuring N differentprecoding matrices for a precoding hopping scheme with an N-slot timeperiod (cycle) has been described. In this case, as the N differentprecoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] areprepared. In the present embodiment, an example of a single carriertransmission scheme has been described, and therefore the case ofarranging symbols in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1]in the time domain (or the frequency domain) has been described. Thepresent invention is not, however, limited in this way, and the Ndifferent precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1]generated in the present embodiment may be adapted to a multi-carriertransmission scheme such as an OFDM transmission scheme or the like. Asin Embodiment 1, as a scheme of adaptation in this case, precodingweights may be changed by arranging symbols in the frequency domain andin the frequency-time domain. Note that a precoding hopping scheme withan N-slot time period (cycle) has been described, but the sameadvantageous effects may be obtained by randomly using N differentprecoding matrices. In other words, the N different precoding matricesdo not necessarily need to be used in a regular period (cycle).

Examples #5 through #10 have been shown based on Conditions #10 through#16. However, in order to achieve a precoding matrix hopping scheme witha longer period (cycle), the period (cycle) for hopping betweenprecoding matrices may be lengthened by, for example, selecting aplurality of examples from Examples #5 through #10 and using theprecoding matrices indicated in the selected examples. For example, aprecoding matrix hopping scheme with a longer period (cycle) may beachieved by using the precoding matrices indicated in Example #7 and theprecoding matrices indicated in Example #10. In this case, Conditions#10 through #16 are not necessarily observed. (In Equation 158 ofCondition #10, Equation 159 of Condition #11, Equation 164 of Condition#13, Equation 175 of Condition #14, and Equation 176 of Condition #15,it becomes important for providing excellent reception quality for theconditions “all x and all y” to be “existing x and existing y”.) Whenviewed from a different perspective, in the precoding matrix hoppingscheme over an N-slot period (cycle) (where N is a large naturalnumber), the probability of providing excellent reception qualityincreases when the precoding matrices of one of Examples #5 through #10are included.

Embodiment 7

The present embodiment describes the structure of a reception device forreceiving modulated signals transmitted by a transmission scheme thatregularly hops between precoding matrices as described in Embodiments1-6.

In Embodiment 1, the following scheme has been described. A transmissiondevice that transmits modulated signals, using a transmission schemethat regularly hops between precoding matrices, transmits informationregarding the precoding matrices. Based on this information, a receptiondevice obtains information on the regular precoding matrix hopping usedin the transmitted frames, decodes the precoding, performs detection,obtains the log-likelihood ratio for the transmitted bits, andsubsequently performs error correction decoding.

The present embodiment describes the structure of a reception device,and a scheme of hopping between precoding matrices, that differ from theabove structure and scheme.

FIG. 40 is an example of the structure of a transmission device in thepresent embodiment. Elements that operate in a similar way to FIG. 3bear the same reference signs. An encoder group (4002) receivestransmission bits (4001) as input. The encoder group (4002), asdescribed in Embodiment 1, includes a plurality of encoders for errorcorrection coding, and based on the frame structure signal 313, acertain number of encoders operate, such as one encoder, two encoders,or four encoders.

When one encoder operates, the transmission bits (4001) are encoded toyield encoded transmission bits. The encoded transmission bits areallocated into two parts, and the encoder group (4002) outputs allocatedbits (4003A) and allocated bits (4003B).

When two encoders operate, the transmission bits (4001) are divided intwo (referred to as divided bits A and B). The first encoder receivesthe divided bits A as input, encodes the divided bits A, and outputs theencoded bits as allocated bits (4003A). The second encoder receives thedivided bits B as input, encodes the divided bits B, and outputs theencoded bits as allocated bits (4003B).

When four encoders operate, the transmission bits (4001) are divided infour (referred to as divided bits A, B, C, and D). The first encoderreceives the divided bits A as input, encodes the divided bits A, andoutputs the encoded bits A. The second encoder receives the divided bitsB as input, encodes the divided bits B, and outputs the encoded bits B.The third encoder receives the divided bits C as input, encodes thedivided bits C, and outputs the encoded bits C. The fourth encoderreceives the divided bits D as input, encodes the divided bits D, andoutputs the encoded bits D. The encoded bits A, B, C, and D are dividedinto allocated bits (4003A) and allocated bits (4003B).

The transmission device supports a transmission scheme such as, forexample, the following Table 1 (Table 1A and Table 1B).

TABLE 1A Number of modulated transmission Pre- signals Error Trans-coding (number of Number correction mission matrix transmit Modulationof coding infor- hopping antennas) scheme encoders scheme mation scheme1 QPSK 1 A 00000000 — B 00000001 — C 00000010 — 16QAM 1 A 00000011 — B00000100 — C 00000101 — 64QAM 1 A 00000110 — B 00000111 — C 00001000 —256QAM  1 A 00001001 — B 00001010 — C 00001011 — 1024QAM  1 A 00001100 —B 00001101 — C 00001110 —

TABLE 1B Number of modulated transmission Pre- signals Error coding(number of Number correction matrix transmit Modulation of en- codingTransmission hopping antennas) scheme coders scheme information scheme 2#1: QPSK, 1 A 00001111 D #2: QPSK B 00010000 D C 00010001 D 2 A 00010010E B 00010011 E C 00010100 E #1: QPSK, 1 A 00010101 D #2: B 00010110 D16QAM C 00010111 D 2 A 00011000 E B 00011001 E C 00011010 E #1: 1 A00011011 D 16QAM, B 00011100 D #2: C 00011101 D 16QAM 2 A 00011110 E B00011111 E C 00100000 E #1: 1 A 00100001 D 16QAM, B 00100010 D #2: C00100011 D 64QAM 2 A 00100100 E B 00100101 E C 00100110 E #1: 1 A00100111 F 64QAM, B 00101000 F #2: C 00101001 F 64QAM 2 A 00101010 G B00101011 G C 00101100 G #1: 1 A 00101101 F 64QAM, B 00101110 F #2: C00101111 F 256QAM 2 A 00110000 G B 00110001 G C 00110010 G #1: 1 A00110011 F 256QAM, B 00110100 F #2: C 00110101 F 256QAM 2 A 00110110 G B00110111 G C 00111000 G 4 A 00111001 H B 00111010 H C 00111011 H #1: 1 A00111100 F 256QAM, B 00111101 F #2: C 00111110 F 1024QAM 2 A 00111111 GB 01000000 G C 01000001 G 4 A 01000010 H B 01000011 H C 01000100 H #1: 1A 01000101 F 1024QAM, B 01000110 F #2: C 01000111 F 1024QAM 2 A 01001000G B 01001001 G C 01001010 G 4 A 01001011 H B 01001100 H C 01001101 H

As shown in Table 1, transmission of a one-stream signal andtransmission of a two-stream signal are supported as the number oftransmission signals (number of transmit antennas). Furthermore, QPSK,16QAM, 64QAM, 256QAM, and 1024QAM are supported as the modulationscheme. In particular, when the number of transmission signals is two,it is possible to set separate modulation schemes for stream #1 andstream #2. For example, “#1: 256QAM, #2: 1024QAM” in Table 1 indicatesthat “the modulation scheme of stream #1 is 256QAM, and the modulationscheme of stream #2 is 1024QAM” (other entries in the table aresimilarly expressed). Three types of error correction coding schemes, A,B, and C, are supported. In this case, A, B, and C may all be differentcoding schemes. A, B, and C may also be different coding rates, and A,B, and C may be coding schemes with different block sizes.

The pieces of transmission information in Table 1 are allocated to modesthat define a “number of transmission signals”, “modulation scheme”,“number of encoders”, and “error correction coding scheme”. Accordingly,in the case of “number of transmission signals: 2”, “modulation scheme:#1: 1024QAM, #2: 1024QAM”, “number of encoders: 4”, and “errorcorrection coding scheme: C”, for example, the transmission informationis set to 01001101. In the frame, the transmission device transmits thetransmission information and the transmission data. When transmittingthe transmission data, in particular when the “number of transmissionsignals” is two, a “precoding matrix hopping scheme” is used inaccordance with Table 1. In Table 1, five types of the “precoding matrixhopping scheme”, D, E, F, G, and H, are prepared. The precoding matrixhopping scheme is set to one of these five types in accordance withTable 1. The following, for example, are ways of implementing the fivedifferent types.

Prepare five different precoding matrices.

Use five different types of period (cycle)s, for example a four-slotperiod (cycle) for D, an eight-slot period (cycle) for E, . . . .

Use both different precoding matrices and different period (cycle)s.

FIG. 41 shows an example of a frame structure of a modulated signaltransmitted by the transmission device in FIG. 40. The transmissiondevice is assumed to support settings for both a mode to transmit twomodulated signals, z1(t) and z2(t), and for a mode to transmit onemodulated signal.

In FIG. 41, the symbol (4100) is a symbol for transmitting the“transmission information” shown in Table 1. The symbols (4101_1) and(4101_2) are reference (pilot) symbols for channel estimation. Thesymbols (4102_1, 4103_1) are data transmission symbols for transmittingthe modulated signal z1(t). The symbols (4102_2, 4103_2) are datatransmission symbols for transmitting the modulated signal z2(t). Thesymbol (4102_1) and the symbol (4102_2) are transmitted at the same timealong the same (shared/common) frequency, and the symbol (4103_1) andthe symbol (4103_2) are transmitted at the same time along the same(shared/common) frequency. The symbols (4102_1, 4103_1) and the symbols(4102_2, 4103_2) are the symbols after precoding matrix calculationusing the scheme of regularly hopping between precoding matricesdescribed in Embodiments 1-4 and Embodiment 6 (therefore, as describedin Embodiment 1, the structure of the streams s1(t) and s2(t) is as inFIG. 6).

Furthermore, in FIG. 41, the symbol (4104) is a symbol for transmittingthe “transmission information” shown in Table 1. The symbol (4105) is areference (pilot) symbol for channel estimation. The symbols (4106,4107) are data transmission symbols for transmitting the modulatedsignal z1(t). The data transmission symbols for transmitting themodulated signal z1(t) are not precoded, since the number oftransmission signals is one.

Accordingly, the transmission device in FIG. 40 generates and transmitsmodulated signals in accordance with Table 1 and the frame structure inFIG. 41. In FIG. 40, the frame structure signal 313 includes informationregarding the “number of transmission signals”, “modulation scheme”,“number of encoders”, and “error correction coding scheme” set based onTable 1. The encoder (4002), the mapping units 306A, B, and theweighting units 308A, B receive the frame structure signal as an inputand operate based on the “number of transmission signals”, “modulationscheme”, “number of encoders”, and “error correction coding scheme” thatare set based on Table 1. “Transmission information” corresponding tothe set “number of transmission signals”, “modulation scheme”, “numberof encoders”, and “error correction coding scheme” is also transmittedto the reception device.

The structure of the reception device may be represented similarly toFIG. 7 of Embodiment 1. The difference with Embodiment 1 is as follows:since the transmission device and the reception device store theinformation in Table 1 in advance, the transmission device does not needto transmit information for regularly hopping between precodingmatrices, but rather transmits “transmission information” correspondingto the “number of transmission signals”, “modulation scheme”, “number ofencoders”, and “error correction coding scheme”, and the receptiondevice obtains information for regularly hopping between precodingmatrices from Table 1 by receiving the “transmission information”.Accordingly, by the control information decoding unit 709 obtaining the“transmission information” transmitted by the transmission device inFIG. 40, the reception device in FIG. 7 obtains, from the informationcorresponding to Table 1, a signal 710 regarding information on thetransmission scheme, as notified by the transmission device, whichincludes information for regularly hopping between precoding matrices.Therefore, when the number of transmission signals is two, the signalprocessing unit 711 can perform detection based on a precoding matrixhopping pattern to obtain received log-likelihood ratios.

Note that in the above description, “transmission information” is setwith respect to the “number of transmission signals”, “modulationscheme”, “number of encoders”, and “error correction coding scheme” asin Table 1, and the precoding matrix hopping scheme is set with respectto the “transmission information”. However, it is not necessary to setthe “transmission information” with respect to the “number oftransmission signals”, “modulation scheme”, “number of encoders”, and“error correction coding scheme”. For example, as in Table 2, the“transmission information” may be set with respect to the “number oftransmission signals” and “modulation scheme”, and the precoding matrixhopping scheme may be set with respect to the “transmissioninformation”.

TABLE 2 Number of modulated Precoding transmission signals matrix(number of transmit Modulation Transmission hopping antennas) schemeinformation scheme 1 QPSK 00000 — 16QAM 00001 — 64QAM 00010 — 256QAM00011 — 1024QAM 00100 — 2 #1: QPSK, 10000 D #2: QPSK #1: QPSK, 10001 E#2: 16QAM #1: 16QAM, 10010 E #2: 16QAM #1: 16QAM, 10011 E #2: 64QAM #1:64QAM, 10100 F #2: 64QAM #1: 64QAM, 10101 F #2: 256QAM #1: 10110 G256QAM, #2: 256QAM #1: 10111 G 256QAM, #2: 1024QAM #1: 11000 H 1024QAM,#2: 1024QAM

In this context, the “transmission information” and the scheme ofsetting the precoding matrix hopping scheme is not limited to Tables 1and 2. As long as a rule is determined in advance for hopping theprecoding matrix hopping scheme based on transmission parameters, suchas the “number of transmission signals”, “modulation scheme”, “number ofencoders”, “error correction coding scheme”, or the like (as long as thetransmission device and the reception device share a predetermined rule,or in other words, if the precoding matrix hopping scheme is hoppedbased on any of the transmission parameters (or on any plurality oftransmission parameters)), the transmission device does not need totransmit information regarding the precoding matrix hopping scheme. Thereception device can identify the precoding matrix hopping scheme usedby the transmission device by identifying the information on thetransmission parameters and can therefore accurately perform decodingand detection. Note that in Tables 1 and 2, a transmission scheme thatregularly hops between precoding matrices is used when the number ofmodulated transmission signals is two, but a transmission scheme thatregularly hops between precoding matrices may be used when the number ofmodulated transmission signals is two or greater.

Accordingly, if the transmission device and reception device share atable regarding transmission patterns that includes information onprecoding hopping schemes, the transmission device need not transmitinformation regarding the precoding hopping scheme, transmitting insteadcontrol information that does not include information regarding theprecoding hopping scheme, and the reception device can infer theprecoding hopping scheme by acquiring this control information.

As described above, in the present embodiment, the transmission devicedoes not transmit information directly related to the scheme ofregularly hopping between precoding matrices. Rather, a scheme has beendescribed wherein the reception device infers information regardingprecoding for the “scheme of regularly hopping between precodingmatrices” used by the transmission device. This scheme yields theadvantageous effect of improved transmission efficiency of data as aresult of the transmission device not transmitting information directlyrelated to the scheme of regularly hopping between precoding matrices.

Note that the present embodiment has been described as changingprecoding weights in the time domain, but as described in Embodiment 1,the present invention may be similarly embodied when using amulti-carrier transmission scheme such as OFDM or the like.

In particular, when the precoding hopping scheme only changes dependingon the number of transmission signals, the reception device can learnthe precoding hopping scheme by acquiring information, transmitted bythe transmission device, on the number of transmission signals.

In the present description, it is considered that acommunications/broadcasting device such as a broadcast station, a basestation, an access point, a terminal, a mobile phone, or the like isprovided with the transmission device, and that a communications devicesuch as a television, radio, terminal, personal computer, mobile phone,access point, base station, or the like is provided with the receptiondevice. Additionally, it is considered that the transmission device andthe reception device in the present description have a communicationsfunction and are capable of being connected via some sort of interfaceto a device for executing applications for a television, radio, personalcomputer, mobile phone, or the like.

Furthermore, in the present embodiment, symbols other than data symbols,such as pilot symbols (preamble, unique word, postamble, referencesymbol, and the like), symbols for control information, and the like maybe arranged in the frame in any way. While the terms “pilot symbol” and“symbols for control information” have been used here, any term may beused, since the function itself is what is important.

It suffices for a pilot symbol, for example, to be a known symbolmodulated with PSK modulation in the transmission and reception devices(or for the reception device to be able to synchronize in order to knowthe symbol transmitted by the transmission device). The reception deviceuses this symbol for frequency synchronization, time synchronization,channel estimation (estimation of Channel State Information (CSI) foreach modulated signal), detection of signals, and the like.

A symbol for control information is for transmitting information otherthan data (of applications or the like) that needs to be transmitted tothe communication partner for achieving communication (for example, themodulation scheme, error correction coding scheme, coding rate of theerror correction coding scheme, setting information in the upper layer,and the like).

Note that the present invention is not limited to the above Embodiments1-5 and may be embodied with a variety of modifications. For example,the above embodiments describe communications devices, but the presentinvention is not limited to these devices and may be implemented assoftware for the corresponding communications scheme.

Furthermore, a precoding hopping scheme used in a scheme of transmittingtwo modulated signals from two antennas has been described, but thepresent invention is not limited in this way. The present invention maybe also embodied as a precoding hopping scheme for similarly changingprecoding weights (matrices) in the context of a scheme whereby fourmapped signals are precoded to generate four modulated signals that aretransmitted from four antennas, or more generally, whereby N mappedsignals are precoded to generate N modulated signals that aretransmitted from N antennas.

In the description, terms such as “precoding” and “precoding weight” areused, but any other terms may be used. What matters in the presentinvention is the actual signal processing.

Different data may be transmitted in streams s1(t) and s2(t), or thesame data may be transmitted.

Each of the transmit antennas of the transmission device and the receiveantennas of the reception device shown in the figures may be formed by aplurality of antennas.

Programs for executing the above transmission scheme may, for example,be stored in advance in Read Only Memory (ROM) and be caused to operateby a Central Processing Unit (CPU).

Furthermore, the programs for executing the above transmission schememay be stored in a computer-readable recording medium, the programsstored in the recording medium may be loaded in the Random Access Memory(RAM) of the computer, and the computer may be caused to operate inaccordance with the programs.

The components in the above embodiments may be typically assembled as aLarge Scale Integration (LSI), a type of integrated circuit. Individualcomponents may respectively be made into discrete chips, or part or allof the components in each embodiment may be made into one chip. While anLSI has been referred to, the terms Integrated Circuit (IC), system LSI,super LSI, or ultra LSI may be used depending on the degree ofintegration. Furthermore, the scheme for assembling integrated circuitsis not limited to LSI, and a dedicated circuit or a general-purposeprocessor may be used. A Field Programmable Gate Array (FPGA), which isprogrammable after the LSI is manufactured, or a reconfigurableprocessor, which allows reconfiguration of the connections and settingsof circuit cells inside the LSI, may be used.

Furthermore, if technology for forming integrated circuits that replacesLSIs emerges, owing to advances in semiconductor technology or toanother derivative technology, the integration of functional blocks maynaturally be accomplished using such technology. The application ofbiotechnology or the like is possible.

Embodiment 8

The present embodiment describes an application of the scheme describedin Embodiments 1-4 and Embodiment 6 for regularly hopping betweenprecoding weights.

FIG. 6 relates to the weighting scheme (precoding scheme) in the presentembodiment. The weighting unit 600 integrates the weighting units 308Aand 308B in FIG. 3. As shown in FIG. 6, the stream s1(t) and the streams2(t) correspond to the baseband signals 307A and 307B in FIG. 3. Inother words, the streams s1(t) and s2(t) are the baseband signalin-phase components I and quadrature components Q when mapped accordingto a modulation scheme such as QPSK, 16QAM, 64QAM, or the like. Asindicated by the frame structure of FIG. 6, the stream s1(t) isrepresented as s1(u) at symbol number u, as s1(u+1) at symbol numberu+1, and so forth. Similarly, the stream s2(t) is represented as s2(u)at symbol number u, as s2(u+1) at symbol number u+1, and so forth. Theweighting unit 600 receives the baseband signals 307A (s1(t)) and 307B(s2(t)) and the information 315 regarding weighting information in FIG.3 as inputs, performs weighting in accordance with the information 315regarding weighting, and outputs the signals 309A (z1(t)) and 309B(z2(t)) after weighting in FIG. 3.

At this point, when for example a precoding matrix hopping scheme withan N=8 period (cycle) as in Example #8 in Embodiment 6 is used, z1(t)and z2(t) are represented as follows.

For symbol number 8i (where i is an integer greater than or equal tozero):

Math 228

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {8i} \right)} \\{z\; 2\left( {8i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\;\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {8i} \right)} \\{s\; 2\left( {8i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 218}\end{matrix}$

Here, j is an imaginary unit, and k=0.

For symbol number 8i+1:

Math 229

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 1} \right)} \\{z\; 2\left( {{8i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\;\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 1} \right)} \\{s\; 2\left( {{8i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 219}\end{matrix}$

Here, k=1.

For symbol number 8i+2:

Math 230

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 2} \right)} \\{z\; 2\left( {{8i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\;\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 2} \right)} \\{s\; 2\left( {{8i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 220}\end{matrix}$

Here, k=2.

For symbol number 8i+3:

Math 231

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 3} \right)} \\{z\; 2\left( {{8i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\;\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 3} \right)} \\{s\; 2\left( {{8i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 221}\end{matrix}$

Here, k=3.

For symbol number 8i+4:

Math 232

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 4} \right)} \\{z\; 2\left( {{8i} + 4} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\;\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 4} \right)} \\{s\; 2\left( {{8i} + 4} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 222}\end{matrix}$

Here, k=4.

For symbol number 8i+5:

Math 233

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 5} \right)} \\{z\; 2\left( {{8i} + 5} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\;\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 5} \right)} \\{s\; 2\left( {{8i} + 5} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 223}\end{matrix}$

Here, k=5.

For symbol number 8i+6:

Math 234

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 6} \right)} \\{z\; 2\left( {{8i} + 6} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\;\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 6} \right)} \\{s\; 2\left( {{8i} + 6} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 224}\end{matrix}$

Here, k=6.

For symbol number 8i+7:

Math 235

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 7} \right)} \\{z\; 2\left( {{8i} + 7} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\;\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 7} \right)} \\{s\; 2\left( {{8i} + 7} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 225}\end{matrix}$

Here, k=7.

The symbol numbers shown here can be considered to indicate time. Asdescribed in other embodiments, in Equation 225, for example, z1(8i+7)and z2(8i+7) at time 8i+7 are signals at the same time, and thetransmission device transmits z1(8i+7) and z2(8i+7) over the same(shared/common) frequency. In other words, letting the signals at time Tbe s1(T), s2(T), z1(T), and z2(T), then z1(T) and z2(T) are sought fromsome sort of precoding matrices and from s1(T) and s2(T), and thetransmission device transmits z1(T) and z2(T) over the same(shared/common) frequency (at the same time). Furthermore, in the caseof using a multi-carrier transmission scheme such as OFDM or the like,and letting signals corresponding to s1, s2, z1, and z2 for (sub)carrierL and time T be s1(T, L), s2(T, L), z1(T, L), and z2(T, L), then z1(T,L) and z2(T, L) are sought from some sort of precoding matrices and froms1(T, L) and s2(T, L), and the transmission device transmits z1(T, L)and z2(T, L) over the same (shared/common) frequency (at the same time).

In this case, the appropriate value of α is given by Equation 198 orEquation 200.

The present embodiment describes a precoding hopping scheme thatincreases period (cycle) size, based on the above-described precodingmatrices of Equation 190.

Letting the period (cycle) of the precoding hopping scheme be 8M, 8Mdifferent precoding matrices are represented as follows.

Math 236

$\begin{matrix}{{F\left\lbrack {{8 \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{k\;\pi}{4\; M}})}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{k\;\pi}{4\; M} + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 226}\end{matrix}$

In this case, i=0, 1, 2, 3, 4, 5, 6, 7, and k=0, 1, . . . , M−2, M−1.

For example, letting M=2 and α<1, the poor reception points for s1 (◯)and for s2 (□) at k=0 are represented as in FIG. 42A. Similarly, thepoor reception points for s1 (◯) and for s2 (□) at k=1 are representedas in FIG. 42B. In this way, based on the precoding matrices in Equation190, the poor reception points are as in FIG. 42A, and by using, as theprecoding matrices, the matrices yielded by multiplying each term in thesecond line on the right-hand side of Equation 190 by e^(jX) (seeEquation 226), the poor reception points are rotated with respect toFIG. 42A (see FIG. 42B). (Note that the poor reception points in FIG.42A and FIG. 42B do not overlap. Even when multiplying by e^(jX), thepoor reception points should not overlap, as in this case. Furthermore,the matrices yielded by multiplying each term in the first line on theright-hand side of Equation 190, rather than in the second line on theright-hand side of Equation 190, by e^(jX) may be used as the precodingmatrices.) In this case, the precoding matrices F[0]−F[15] arerepresented as follows.

Math 237

$\begin{matrix}{{F\left\lbrack {{8 \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + {Xk}})}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + {Xk} + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 227}\end{matrix}$

Here, i=0, 1, 2, 3, 4, 5, 6, 7, and k=0, 1.

In this case, when M=2, precoding matrices F[0]−F[15] are generated (theprecoding matrices F[0]−F[15] may be in any order, and the matricesF[0]−F[15] may each be different). Symbol number 16i may be precodedusing F[0], symbol number 16i+1 may be precoded using F[1], . . . , andsymbol number 16i+h may be precoded using F[h], for example (h=0, 1, 2,. . . , 14, 15). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.)

Summarizing the above considerations, with reference to Equations 82-85,N-period (cycle) precoding matrices are represented by the followingequation.

Math 238

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{(i)}}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 228}\end{matrix}$

Here, since the period (cycle) has N slots, i=0, 1, 2, . . . , N−2, N−1.

Furthermore, the N×M period (cycle) precoding matrices based on Equation228 are represented by the following equation.

Math 239

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + X_{k}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + X_{k} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 229}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1, and k⁼0, 1, . . . , M−2, M−1.

Precoding matrices F[0]−F[N×M−1] are thus generated (the precodingmatrices F[0]−F[N×M−1] may be in any order for the N×M slots in theperiod (cycle)). Symbol number N×M×i may be precoded using F[0], symbolnumber N×M×i+1 may be precoded using F[1], . . . , and symbol numberN×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . ,N×M−2, N×M−1). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality. Note that while the N×M period(cycle) precoding matrices have been set to Equation 229, the N×M period(cycle) precoding matrices may be set to the following equation, asdescribed above.

Math 240

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j{({{\theta_{11}{(i)}} + X_{k}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + X_{k} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 230}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1, and k⁼0, 1, . . . , M−2, M−1.

In Equations 229 and 230, when 0 radians≦δ<2π radians, the matrices area unitary matrix when δ=π radians and are a non-unitary matrix when δ ≠πradians. In the present scheme, use of a non-unitary matrix for π/2radians≦|δ|<π radians is one characteristic structure (the conditionsfor δ being similar to other embodiments), and excellent data receptionquality is obtained. Use of a unitary matrix is another structure, andas described in detail in Embodiment 10 and Embodiment 16, if N is anodd number in Equations 229 and 230, the probability of obtainingexcellent data reception quality increases.

Embodiment 9

The present embodiment describes a scheme for regularly hopping betweenprecoding matrices using a unitary matrix.

As described in Embodiment 8, in the scheme of regularly hopping betweenprecoding matrices over a period (cycle) with N slots, the precodingmatrices prepared for the N slots with reference to Equations 82-85 arerepresented as follows.

Math 241

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 231}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. (Let α>0.) Since a unitarymatrix is used in the present embodiment, the precoding matrices inEquation 231 may be represented as follows.

Math 242

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{{\alpha^{2} + 1}\;}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 232}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. (Let α>0.) From Condition #5(Math 106) and Condition #6 (Math 107) in Embodiment 3, the followingcondition is important for achieving excellent data reception quality.

Math 243

Condition #17e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

-   -   (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1;        and x≠y.)        Math 244        Condition #18        e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹        ^((y)−π)) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)    -   (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1;        and x≠y.)

Embodiment 6 describes the distance between poor reception points. Inorder to increase the distance between poor reception points, it isimportant for the number of slots N to be an odd number three orgreater. The following explains this point.

In order to distribute the poor reception points evenly with regards tophase in the complex plane, as described in Embodiment 6, Condition #19and Condition #20 are provided.

Math 245

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {{\mathbb{e}}^{j{(\frac{2\pi}{N})}}\mspace{14mu}{for}}}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}} & {{Condition}\mspace{14mu}{\# 19}}\end{matrix}$Math 246

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {{\mathbb{e}}^{j{({- \frac{2\pi}{N}})}}\mspace{14mu}{for}}}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}} & {{Condition}\mspace{14mu}{\# 20}}\end{matrix}$

In other words, Condition #19 means that the difference in phase is 2π/Nradians. On the other hand, Condition #20 means that the difference inphase is −2π/N radians.

Letting θ₁₁(0)−θ₂₁(0)=0 radians, and letting α<1, the distribution ofpoor reception points for s1 and for s2 in the complex plane for an N=3period (cycle) is shown in FIG. 43A, and the distribution of poorreception points for s1 and for s2 in the complex plane for an N=4period (cycle) is shown in FIG. 43B. Letting θ₁₁(0)−θ₂₁(0)=0 radians,and letting α>1, the distribution of poor reception points for s1 andfor s2 in the complex plane for an N=3 period (cycle) is shown in FIG.44A, and the distribution of poor reception points for s1 and for s2 inthe complex plane for an N=4 period (cycle) is shown in FIG. 44B.

In this case, when considering the phase between a line segment from theorigin to a poor reception point and a half line along the real axisdefined by real ≧0 (see FIG. 43A), then for either α>1 or α<1, when N=4,the case always occurs wherein the phase for the poor reception pointsfor s1 and the phase for the poor reception points for s2 are the samevalue. (See 4301, 4302 in FIG. 43B, and 4401, 4402 in FIG. 44B.) In thiscase, in the complex plane, the distance between poor reception pointsbecomes small. On the other hand, when N=3, the phase for the poorreception points for s1 and the phase for the poor reception points fors2 are never the same value.

Based on the above, considering how the case always occurs wherein thephase for the poor reception points for s1 and the phase for the poorreception points for s2 are the same value when the number of slots N inthe period (cycle) is an even number, setting the number of slots N inthe period (cycle) to an odd number increases the probability of agreater distance between poor reception points in the complex plane ascompared to when the number of slots N in the period (cycle) is an evennumber. However, when the number of slots N in the period (cycle) issmall, for example when N≦16, the minimum distance between poorreception points in the complex plane can be guaranteed to be a certainlength, since the number of poor reception points is small. Accordingly,when N≦16, even if N is an even number, cases do exist where datareception quality can be guaranteed.

Therefore, in the scheme for regularly hopping between precodingmatrices based on Equation 232, when the number of slots N in the period(cycle) is set to an odd number, the probability of improving datareception quality is high. Precoding matrices F[0]−F[N−1] are generatedbased on Equation 232 (the precoding matrices F[0]−F[N−1] may be in anyorder for the N slots in the period (cycle)). Symbol number Ni may beprecoded using F[0], symbol number Ni+1 may be precoded using F[1], . .. , and symbol number N×i+h may be precoded using F[h], for example(h=0, 1, 2, . . . , N−2, N−1). (In this case, as described in previousembodiments, precoding matrices need not be hopped between regularly.)Furthermore, when the modulation scheme for both s1 and s2 is 16QAM, ifα is set as follows,

Math 247

$\begin{matrix}{\alpha = \frac{\sqrt{2} + 4}{\sqrt{2} + 2}} & {{Equation}\mspace{14mu} 233}\end{matrix}$

the advantageous effect of increasing the minimum distance between16×16=256 signal points in the I-Q plane for a specific LOS environmentmay be achieved.

In the present embodiment, the scheme of structuring N differentprecoding matrices for a precoding hopping scheme with an N-slot timeperiod (cycle) has been described. In this case, as the N differentprecoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] areprepared. In the present embodiment, an example of a single carriertransmission scheme has been described, and therefore the case ofarranging symbols in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1]in the time domain (or the frequency domain) has been described. Thepresent invention is not, however, limited in this way, and the Ndifferent precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1]generated in the present embodiment may be adapted to a multi-carriertransmission scheme such as an OFDM transmission scheme or the like. Asin Embodiment 1, as a scheme of adaption in this case, precoding weightsmay be changed by arranging symbols in the frequency domain and in thefrequency-time domain. Note that a precoding hopping scheme with anN-slot time period (cycle) has been described, but the same advantageouseffects may be obtained by randomly using N different precodingmatrices. In other words, the N different precoding matrices do notnecessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slotsN in the period (cycle) of the above scheme of regularly hopping betweenprecoding matrices), when the N different precoding matrices of thepresent embodiment are included, the probability of excellent receptionquality increases. In this case, Condition #17 and Condition #18 can bereplaced by the following conditions. (The number of slots in the period(cycle) is considered to be N.)

Math 248

Condition #17′e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 249Condition #18′e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π) for)∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

-   -   (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1;        and x≠y.)

Embodiment 10

The present embodiment describes a scheme for regularly hopping betweenprecoding matrices using a unitary matrix that differs from the examplein Embodiment 9.

In the scheme of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

Math 250

$\begin{matrix}{{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 234}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0.

Math 251

$\begin{matrix}{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{{j\theta}_{11}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 235}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. (Let the α inEquation 234 and the α in Equation 235 be the same value.)

From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment3, the following conditions are important in Equation 234 for achievingexcellent data reception quality.

Math 252

$\begin{matrix}{{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}} \neq {{\mathbb{e}}^{j{({{\theta_{11}{(y)}} - {\theta_{21}{(y)}}})}}\mspace{14mu}{for}}}{{\forall x},{\forall{y\left( {{{x \neq y};x},{y = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - 1}} \right)}}}} & {{Condition}\mspace{14mu}{\# 21}}\end{matrix}$

-   -   (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1;        and x≠y.)        Math 253        Condition #22        e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹        ^((y)−π)) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)        (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1;        and x≠y.)

Addition of the following condition is considered.

Math 254

Condition #23θ₁₁(x)=θ₁₁(x+N) for ∀x(x=0,1,2, . . . ,N−2,N−1)andθ₂₁(y)=θ₂₁(y+N) for ∀y(y=0,1,2, . . . ,N−2,N−1)

Next, in order to distribute the poor reception points evenly withregards to phase in the complex plane, as described in Embodiment 6,Condition #24 and Condition #25 are provided.

Math 255

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {{\mathbb{e}}^{j{(\frac{2\pi}{N})}}\mspace{14mu}{for}}}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}} & {{Condition}\mspace{14mu}{\# 24}}\end{matrix}$Math 256

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {{\mathbb{e}}^{j{({- \frac{2\pi}{N}})}}\mspace{14mu}{for}}}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}} & {{Condition}\mspace{14mu}{\# 25}}\end{matrix}$

In other words, Condition #24 means that the difference in phase is 2π/Nradians. On the other hand, Condition #25 means that the difference inphase is −2π/N radians.

Letting θ₁₁(0)−θ₂₁(0)=0 radians, and letting α>1, the distribution ofpoor reception points for s1 and for s2 in the complex plane when N=4 isshown in FIGS. 45A and 45B. As is clear from FIGS. 45A and 45B, in thecomplex plane, the minimum distance between poor reception points for s1is kept large, and similarly, the minimum distance between poorreception points for s2 is also kept large. Similar conditions arecreated when α<1. Furthermore, making the same considerations as inEmbodiment 9, the probability of a greater distance between poorreception points in the complex plane increases when N is an odd numberas compared to when N is an even number. However, when N is small, forexample when N≦16, the minimum distance between poor reception points inthe complex plane can be guaranteed to be a certain length, since thenumber of poor reception points is small. Accordingly, when N≦16, evenif N is an even number, cases do exist where data reception quality canbe guaranteed.

Therefore, in the scheme for regularly hopping between precodingmatrices based on Equations 234 and 235, when N is set to an odd number,the probability of improving data reception quality is high. Precodingmatrices F[0]−F[2N−1] are generated based on Equations 234 and 235 (theprecoding matrices F[0]−F[2N−1] may be arranged in any order for the 2Nslots in the period (cycle)). Symbol number 2Ni may be precoded usingF[0], symbol number 2Ni+1 may be precoded using F[1], . . . , and symbolnumber 2N×i+h may be precoded using F[h], for example (h=0, 1, 2, . . ., 2N−2, 2N−1). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.) Furthermore,when the modulation scheme for both s1 and s2 is 16QAM, if α is set asin Equation 233, the advantageous effect of increasing the minimumdistance between 16×16=256 signal points in the I-Q plane for a specificLOS environment may be achieved.

The following conditions are possible as conditions differing fromCondition #23:

Math 257

Condition #26e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)

-   -   (where x is N, N+1,N+2, . . . , 2N−2, 2N−1; y is N, N+1,N+2, . .        . , 2N−2, 2N−1; and x≠y.)        Math 258        Condition #27        e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹        ^((y)−π)) for ∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)    -   (where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, .        . . , 2N−2, 2N˜1; and x≠y.)

In this case, by satisfying Condition #21, Condition #22, Condition #26,and Condition #27, the distance in the complex plane between poorreception points for s1 is increased, as is the distance between poorreception points for s2, thereby achieving excellent data receptionquality.

In the present embodiment, the scheme of structuring 2N differentprecoding matrices for a precoding hopping scheme with a 2N-slot timeperiod (cycle) has been described. In this case, as the 2N differentprecoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] areprepared. In the present embodiment, an example of a single carriertransmission scheme has been described, and therefore the case ofarranging symbols in the order F[0], F[1], F[2], . . . , F[2N−2],F[2N−1] in the time domain (or the frequency domain) has been described.The present invention is not, however, limited in this way, and the 2Ndifferent precoding matrices F[0], F[1], F[2], . . . , F[2N−2], F[2N−1]generated in the present embodiment may be adapted to a multi-carriertransmission scheme such as an OFDM transmission scheme or the like. Asin Embodiment 1, as a scheme of adaption in this case, precoding weightsmay be changed by arranging symbols in the frequency domain and in thefrequency-time domain. Note that a precoding hopping scheme with a2N-slot time period (cycle) has been described, but the sameadvantageous effects may be obtained by randomly using 2N differentprecoding matrices. In other words, the 2N different precoding matricesdo not necessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slots2N in the period (cycle) of the above scheme of regularly hoppingbetween precoding matrices), when the 2N different precoding matrices ofthe present embodiment are included, the probability of excellentreception quality increases.

Embodiment 11

The present embodiment describes a scheme for regularly hopping betweenprecoding matrices using a non-unitary matrix.

In the scheme of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

Math 259

$\begin{matrix}{{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 236}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. Furthermore, letδ≠π radians.

Math 260

$\begin{matrix}{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} & {\mathbb{e}}^{{j\theta}_{11}{(i)}} \\{\mathbb{e}}^{j{({{\theta_{21}\;{(i)}} + \lambda + \delta})}} & {\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 237}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. (Let the α inEquation 236 and the α in Equation 237 be the same value.)

From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment3, the following conditions are important in Equation 236 for achievingexcellent data reception quality.

Math 261

Condition #28e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

-   -   (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1;        and x≠y.)        Math 262        Condition #29        e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−δ)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹        ^((y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)    -   (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1;        and x≠y.)

Addition of the following condition is considered.

Math 263

Condition #30θ₁₁(x)=θ₁₁(x+N) for ∀x(x=0,1,2, . . . ,N−2,N−1)andθ₂₁(y)=θ₂₁(y+N) for ∀y(y=0,1,2, . . . ,N−2,N−1)

Note that instead of Equation 237, the precoding matrices in thefollowing Equation may be provided.

Math 264

$\begin{matrix}\begin{matrix}{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}} \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;{\theta_{11}{(i)}}}} & {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{(i)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda - \delta})}}}\end{pmatrix}}}\end{matrix} & {{Equation}\mspace{14mu} 238}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. (Let the α inEquation 236 and the α in Equation 238 be the same value.)

As an example, in order to distribute the poor reception points evenlywith regards to phase in the complex plane, as described in Embodiment6, Condition #31 and Condition #32 are provided.

Math 265

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{(\frac{2\;\pi}{N})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 31}}\end{matrix}$Math 266

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\;\pi}{N}})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 32}}\end{matrix}$

In other words, Condition #31 means that the difference in phase is 2π/Nradians. On the other hand, Condition #32 means that the difference inphase is −2π/N radians.

Letting θ₁₁(0)−θ₂₁(0)=0 radians, letting α>1, and letting 6=(3π)/4radians, the distribution of poor reception points for s1 and for s2 inthe complex plane when N=4 is shown in FIGS. 46A and 46B. With thesesettings, the period (cycle) for hopping between precoding matrices isincreased, and the minimum distance between poor reception points fors1, as well as the minimum distance between poor reception points fors2, in the complex plane is kept large, thereby achieving excellentreception quality. An example in which α>1, 6=(3π)/4 radians, and N=4has been described, but the present invention is not limited in thisway. Similar advantageous effects may be obtained for π/2 radians≦|δ|<πradians, α>0, and α≠1.

The following conditions are possible as conditions differing fromCondition #30:

Math 267

Condition #33e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1,N+2, . . . ,2N−2, 2N−1; and x≠y.)Math 268Condition #34e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=N,N+1+2, . . . ,2N−2,2N−1)(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . ,2N−2, 2N−1; and x≠y.)

In this case, by satisfying Condition #28, Condition #29, Condition #33,and Condition #34, the distance in the complex plane between poorreception points for s1 is increased, as is the distance between poorreception points for s2, thereby achieving excellent data receptionquality.

In the present embodiment, the scheme of structuring 2N differentprecoding matrices for a precoding hopping scheme with a 2N-slot timeperiod (cycle) has been described. In this case, as the 2N differentprecoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] areprepared. In the present embodiment, an example of a single carriertransmission scheme has been described, and therefore the case ofarranging symbols in the order F[0], F[1], F[2], . . . , F[2N−2],F[2N−1] in the time domain (or the frequency domain) has been described.The present invention is not, however, limited in this way, and the 2Ndifferent precoding matrices F[0], F[1], F[2], . . . , F[2N−2], F[2N−1]generated in the present embodiment may be adapted to a multi-carriertransmission scheme such as an OFDM transmission scheme or the like. Asin Embodiment 1, as a scheme of adaption in this case, precoding weightsmay be changed by arranging symbols in the frequency domain and in thefrequency-time domain. Note that a precoding hopping scheme with a2N-slot time period (cycle) has been described, but the sameadvantageous effects may be obtained by randomly using 2N differentprecoding matrices. In other words, the 2N different precoding matricesdo not necessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slots2N in the period (cycle) of the above scheme of regularly hoppingbetween precoding matrices), when the 2N different precoding matrices ofthe present embodiment are included, the probability of excellentreception quality increases.

Embodiment 12

The present embodiment describes a scheme for regularly hopping betweenprecoding matrices using a non-unitary matrix.

In the scheme of regularly hopping between precoding matrices over aperiod (cycle) with N slots, the precoding matrices prepared for the Nslots are represented as follows.

Math 269

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{(i)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{(i)}}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 239}\end{matrix}$Let α be a fixed value (not depending on i), where α>0. Furthermore, letδ≠π radians (a fixed value not depending on i), and i=0, 1, 2, . . . ,N−2, N−1.

From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment3, the following conditions are important in Equation 239 for achievingexcellent data reception quality.

Math 270

Condition #35e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 271Condition #36e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−δ)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−δ)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

As an example, in order to distribute the poor reception points evenlywith regards to phase in the complex plane, as described in Embodiment6, Condition #37 and Condition #38 are provided.

Math 272

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{(\frac{2\;\pi}{N})}}}{{for}\mspace{11mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 37}}\end{matrix}$Math 273

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\;\pi}{N}})}}}{{for}\mspace{11mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 38}}\end{matrix}$

In other words, Condition #37 means that the difference in phase is 2π/Nradians. On the other hand, Condition #38 means that the difference inphase is −2π/N radians.

In this case, if π/2 radians≦|δ|<π radians, α>0, and α≠1, the distancein the complex plane between poor reception points for s1 is increased,as is the distance between poor reception points for s2, therebyachieving excellent data reception quality. Note that Condition #37 andCondition #38 are not always necessary.

In the present embodiment, the scheme of structuring N differentprecoding matrices for a precoding hopping scheme with an N-slot timeperiod (cycle) has been described. In this case, as the N differentprecoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] areprepared. In the present embodiment, an example of a single carriertransmission scheme has been described, and therefore the case ofarranging symbols in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1]in the time domain (or the frequency domain) has been described. Thepresent invention is not, however, limited in this way, and the Ndifferent precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1]generated in the present embodiment may be adapted to a multi-carriertransmission scheme such as an OFDM transmission scheme or the like. Asin Embodiment 1, as a scheme of adaption in this case, precoding weightsmay be changed by arranging symbols in the frequency domain and in thefrequency-time domain. Note that a precoding hopping scheme with anN-slot time period (cycle) has been described, but the same advantageouseffects may be obtained by randomly using N different precodingmatrices. In other words, the N different precoding matrices do notnecessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slotsN in the period (cycle) of the above scheme of regularly hopping betweenprecoding matrices), when the N different precoding matrices of thepresent embodiment are included, the probability of excellent receptionquality increases. In this case, Condition #35 and Condition #36 can bereplaced by the following conditions. (The number of slots in the period(cycle) is considered to be N.)

Math 274

Condition #35′e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 275Condition #36′e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−δ)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−δ)) for∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Embodiment 13

The present embodiment describes a different example than Embodiment 8.

In the scheme of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

Math 276

$\begin{matrix}{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}} & {{Equation}\mspace{14mu} 240} \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{(i)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{(i)}}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}}\end{pmatrix}}} & \;\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. Furthermore, letδ≠π radians.

Math 277

$\begin{matrix}{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}} & {{Equation}\mspace{14mu} 241} \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} & {\mathbb{e}}^{j\;{\theta_{11}{(i)}}} \\{\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}} & {\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{(i)}}}}\end{pmatrix}}} & \;\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. (Let the α inEquation 240 and the α in Equation 241 be the same value.)

Furthermore, the 2×N×M period (cycle) precoding matrices based onEquations 240 and 241 are represented by the following equations.

Math 278

$\begin{matrix}{\mspace{79mu}{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}} & {{Equation}\mspace{14mu} 242} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{(i)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j(\;{{\theta_{21}{(i)}} + X_{k}})}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + X_{k} + \lambda + \delta})}}\end{pmatrix}}} & \;\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

Math 279

$\begin{matrix}{\mspace{79mu}{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}} & {{Equation}\mspace{14mu} 243} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} & {\mathbb{e}}^{j\;{\theta_{11}{(i)}}} \\{\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta + Y_{k}})}} & {\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({i + Y_{k}})}}}\end{pmatrix}}} & \;\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1. Furthermore, Xk=Yk may be true,or Xk≠Yk may be true.

Precoding matrices F[0]−F[2×N×M−1] are thus generated (the precodingmatrices F[0]−F[2×N×M−1] may be in any order for the 2×N×M slots in theperiod (cycle)). Symbol number 2×N×M×i may be precoded using F[0],symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbolnumber 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . .. , 2×N×M−2, 2×N×M−1). (In this case, as described in previousembodiments, precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality.

The 2×N×M period (cycle) precoding matrices in Equation 242 may bechanged to the following equation.

Math 280

$\begin{matrix}{\mspace{79mu}{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}} & {{Equation}\mspace{14mu} 244} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j{({{\theta_{11}{(i)}} + X_{k}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + X_{k} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{(i)}}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}}\end{pmatrix}}} & \;\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

The 2×N×M period (cycle) precoding matrices in Equation 243 may also bechanged to any of Equations 245-247.

Math 281

$\begin{matrix}{\mspace{79mu}{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}} & {{Equation}\mspace{14mu} 245} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda + Y_{k}})}}} & {\mathbb{e}}^{j\;{\theta_{11}{({i + Y_{k}})}}} \\{\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}} & {\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{(i)}}}}\end{pmatrix}}} & \;\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

Math 282

$\begin{matrix}{\mspace{85mu}{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}} & {{Equation}\mspace{14mu} 246} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;{\theta_{11}{(i)}}}} & {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({i + Y_{k}})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta + Y_{k}})}}}\end{pmatrix}}} & \;\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

Math 283

$\begin{matrix}{\mspace{79mu}{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}} & {{Equation}\mspace{14mu} 247} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;{\theta_{11}{({i + Y_{k}})}}}} & {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda + Y_{k}})}} \\{\mathbb{e}}^{j\;{\theta_{21}{(i)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda - \delta})}}}\end{pmatrix}}} & \;\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

Focusing on poor reception points, if Equations 242 through 247 satisfythe following conditions,

Math 284

Condition #39e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

-   -   (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1;        and x≠y.)        Math 285        Condition #40        e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−δ)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹        ^((y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)    -   (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1;        and x≠y.)        Math 286        Condition #41        θ₁₁(x)=θ₁₁(x+N) for ∀_(x)(x=0,1,2, . . . ,N−2,N−1)        and        θ₂₁(y)=θ₂₁(y+N) for ∀y(y=0,1,2, . . . ,N−2,N−1)

then excellent data reception quality is achieved. Note that inEmbodiment 8, Condition #39 and Condition #40 should be satisfied.

Focusing on Xk and Yk, if Equations 242 through 247 satisfy thefollowing conditions,

Math 287

Condition #42X _(a) ≠X _(b)+2×s×π for ∀a,∀b(a≠b;a,b=0,1,2, . . . ,M−2,M−1)

(a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1; anda≠b.)

(Here, s is an integer.)

Math 288

Condition #43Y _(a) ≠Y _(b)+2×u×π for ∀a,∀b(a≠b;a,b=0,1,2, . . . ,M−2,M−1)(a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1; anda≠b.)

(Here, u is an integer.)

then excellent data reception quality is achieved. Note that inEmbodiment 8, Condition #42 should be satisfied.

In Equations 242 and 247, when 0 radians≦δ<2π radians, the matrices area unitary matrix when δ=π radians and are a non-unitary matrix when δ≠πradians. In the present scheme, use of a non-unitary matrix for π/2radians≦|δ|<π radians is one characteristic structure, and excellentdata reception quality is obtained. Use of a unitary matrix is anotherstructure, and as described in detail in Embodiment 10 and Embodiment16, if N is an odd number in Equations 242 through 247, the probabilityof obtaining excellent data reception quality increases.

Embodiment 14

The present embodiment describes an example of differentiating betweenusage of a unitary matrix and a non-unitary matrix as the precodingmatrix in the scheme for regularly hopping between precoding matrices.

The following describes an example that uses a two-by-two precodingmatrix (letting each element be a complex number), i.e. the case whentwo modulated signals (s1(t) and s2(t)) that are based on a modulationscheme are precoded, and the two precoded signals are transmitted by twoantennas.

When transmitting data using a scheme of regularly hopping betweenprecoding matrices, the mapping units 306A and 306B in the transmissiondevice in FIG. 3 and FIG. 13 hop the modulation scheme in accordancewith the frame structure signal 313. The relationship between themodulation level (the number of signal points for the modulation schemein the I-Q plane) of the modulation scheme and the precoding matrices isdescribed.

The advantage of the scheme of regularly hopping between precodingmatrices is that, as described in Embodiment 6, excellent data receptionquality is achieved in an LOS environment. In particular, when thereception device performs ML calculation or applies APP (or Max-log APP)based on ML calculation, the advantageous effect is considerable.Incidentally, ML calculation greatly impacts circuit scale (calculationscale) in accordance with the modulation level of the modulation scheme.For example, when two precoded signals are transmitted from twoantennas, and the same modulation scheme is used for two modulatedsignals (signals based on the modulation scheme before precoding), thenumber of candidate signal points in the I-Q plane (received signalpoints 1101 in FIG. 11) is 4×4=16 when the modulation scheme is QPSK,16×16=256 when the modulation scheme is 16QAM, 64×64=4096 when themodulation scheme is 64QAM, 256×256=65,536 when the modulation scheme is256QAM, and 1024×1024=1,048,576 when the modulation scheme is 256QAM. Inorder to keep the calculation scale of the reception device down to acertain circuit size, when the modulation scheme is QPSK, 16QAM, or64QAM, ML calculation ((Max-log) APP based on ML calculation) is used,and when the modulation scheme is 256QAM or 1024QAM, linear operationsuch as MMSE or ZF is used in the reception device. (In some cases, MLcalculation may be used for 256QAM.)

When such a reception device is assumed, consideration of theSignal-to-Noise Power Ratio (SNR) after separation of multiple signalsindicates that a unitary matrix is appropriate as the precoding matrixwhen the reception device performs linear operation such as MMSE or ZF,whereas either a unitary matrix or a non-unitary matrix may be used whenthe reception device performs ML calculation. Taking any of the aboveembodiments into consideration, when two precoded signals aretransmitted from two antennas, the same modulation scheme is used fortwo modulated signals (signals based on the modulation scheme beforeprecoding), a non-unitary matrix is used as the precoding matrix in thescheme for regularly hopping between precoding matrices, the modulationlevel of the modulation scheme is equal to or less than 64 (or equal toor less than 256), and a unitary matrix is used when the modulationlevel is greater than 64 (or greater than 256), then for all of themodulation schemes supported by the transmission system, there is anincreased probability of achieving the advantageous effect wherebyexcellent data reception quality is achieved for any of the modulationschemes while reducing the circuit scale of the reception device.

When the modulation level of the modulation scheme is equal to or lessthan 64 (or equal to or less than 256) as well, in some cases use of aunitary matrix may be preferable. Based on this consideration, when aplurality of modulation schemes are supported in which the modulationlevel is equal to or less than 64 (or equal to or less than 256), it isimportant that in some cases, in some of the plurality of supportedmodulation schemes where the modulation level is equal to or less than64, a non-unitary matrix is used as the precoding matrix in the schemefor regularly hopping between precoding matrices.

The case of transmitting two precoded signals from two antennas has beendescribed above as an example, but the present invention is not limitedin this way. In the case when N precoded signals are transmitted from Nantennas, and the same modulation scheme is used for N modulated signals(signals based on the modulation scheme before precoding), a thresholdβ_(N) may be established for the modulation level of the modulationscheme. When a plurality of modulation schemes for which the modulationlevel is equal to or less than β_(N) are supported, in some of theplurality of supported modulation schemes where the modulation level isequal to or less than β_(N), a non-unitary matrix is used as theprecoding matrices in the scheme for regularly hopping between precodingmatrices, whereas for modulation schemes for which the modulation levelis greater than β_(N), a unitary matrix is used. In this way, for all ofthe modulation schemes supported by the transmission system, there is anincreased probability of achieving the advantageous effect wherebyexcellent data reception quality is achieved for any of the modulationschemes while reducing the circuit scale of the reception device. (Whenthe modulation level of the modulation scheme is equal to or less thanβ_(N), a non-unitary matrix may always be used as the precoding matrixin the scheme for regularly hopping between precoding matrices.)

In the above description, the same modulation scheme has been describedas being used in the modulation scheme for simultaneously transmitting Nmodulated signals. The following, however, describes the case in whichtwo or more modulation schemes are used for simultaneously transmittingN modulated signals.

As an example, the case in which two precoded signals are transmitted bytwo antennas is described. The two modulated signals (signals based onthe modulation scheme before precoding) are either modulated with thesame modulation scheme, or when modulated with different modulationschemes, are modulated with a modulation scheme having a modulationlevel of 2^(a1) or a modulation level of 2^(a2). In this case, when thereception device uses ML calculation ((Max-log) APP based on MLcalculation), the number of candidate signal points in the I-Q plane(received signal points 1101 in FIG. 11) is 2^(a1)×2^(a2)=2^(a1+a2). Asdescribed above, in order to achieve excellent data reception qualitywhile reducing the circuit scale of the reception device, a threshold2^(β) may be provided for 2^(a1+a2), and when 2^(a1+a2)≦2^(β), anon-unitary matrix may be used as the precoding matrix in the scheme forregularly hopping between precoding matrices, whereas a unitary matrixmay be used when 2^(a1+a2)>2^(β).

Furthermore, when 2^(a1+a2)≦2^(β), in some cases use of a unitary matrixmay be preferable. Based on this consideration, when a plurality ofcombinations of modulation schemes are supported for which2^(a1+a2)≦2^(β), it is important that in some of the supportedcombinations of modulation schemes for which 2^(a1+a2)≦2^(β), anon-unitary matrix is used as the precoding matrix in the scheme forregularly hopping between precoding matrices.

As an example, the case in which two precoded signals are transmitted bytwo antennas has been described, but the present invention is notlimited in this way. For example, N modulated signals (signals based onthe modulation scheme before precoding) may be either modulated with thesame modulation scheme or, when modulated with different modulationschemes, the modulation level of the modulation scheme for the i^(th)modulated signal may be 2^(ai) (where i=1, 2, . . . , N−1, N).

In this case, when the reception device uses ML calculation ((Max-log)APP based on ML calculation), the number of candidate signal points inthe I-Q plane (received signal points 1101 in FIG. 11) is 2^(a1)×2^(a2)×. . . ×2^(a1)× . . . ×2^(aN)=2^(a1+a2+ . . . +ai+ . . . +aN). Asdescribed above, in order to achieve excellent data reception qualitywhile reducing the circuit scale of the reception device, a threshold2^(β) may be provided for 2^(a1+a2+ . . . +ai+ . . . +aN).

Math 289

$\begin{matrix}{{2^{{a\; 1} + {a\; 2} + \;\ldots\; + {ai} + \;\ldots\; + {aN}} = {2^{Y} \leq 2^{\beta}}}{where}{Y = {\sum\limits_{i = 1}^{N}a_{i}}}} & {{Condition}\mspace{14mu}{\# 44}}\end{matrix}$When a plurality of combinations of a modulation schemes satisfyingCondition #44 are supported, in some of the supported combinations ofmodulation schemes satisfying Condition #44, a non-unitary matrix isused as the precoding matrix in the scheme for regularly hopping betweenprecoding matrices.Math 290

$\begin{matrix}{{2^{{a\; 1} + {a\; 2} + \;\ldots\; + {ai}\; + \;\ldots\; + {aN}} = {2^{Y} > 2^{\beta}}}{where}{Y = {\sum\limits_{i = 1}^{N}a_{i}}}} & {{Condition}\mspace{14mu}{\# 45}}\end{matrix}$

By using a unitary matrix in all of the combinations of modulationschemes satisfying Condition #45, then for all of the modulation schemessupported by the transmission system, there is an increased probabilityof achieving the advantageous effect whereby excellent data receptionquality is achieved while reducing the circuit scale of the receptiondevice for any of the combinations of modulation schemes. (A non-unitarymatrix may be used as the precoding matrix in the scheme for regularlyhopping between precoding matrices in all of the supported combinationsof modulation schemes satisfying Condition #44.)

Embodiment 15

The present embodiment describes an example of a system that adopts ascheme for regularly hopping between precoding matrices using amulti-carrier transmission scheme such as OFDM.

FIGS. 47A and 47B show an example according to the present embodiment offrame structure in the time and frequency domains for a signaltransmitted by a broadcast station (base station) in a system thatadopts a scheme for regularly hopping between precoding matrices using amulti-carrier transmission scheme such as OFDM. (The frame structure isset to extend from time $1 to time $T.) FIG. 47A shows the framestructure in the time and frequency domains for the stream s1 describedin Embodiment 1, and FIG. 47B shows the frame structure in the time andfrequency domains for the stream s2 described in Embodiment 1. Symbolsat the same time and the same (sub)carrier in stream s1 and stream s2are transmitted by a plurality of antennas at the same time and the samefrequency.

In FIGS. 47A and 47B, the (sub)carriers used when using OFDM are dividedas follows: a carrier group #A composed of (sub)carrier a−(sub)carriera+Na, a carrier group #B composed of (sub)carrier b−(sub)carrier b+Nb, acarrier group #C composed of (sub)carrier c−(sub)carrier c+Nc, a carriergroup #D composed of (sub)carrier d−(sub)carrier d+Nd, . . . . In eachsubcarrier group, a plurality of transmission schemes are assumed to besupported. By supporting a plurality of transmission schemes, it ispossible to effectively capitalize on the advantages of the transmissionschemes. For example, in FIGS. 47A and 47B, a spatial multiplexing MIMOsystem, or a MIMO system with a fixed precoding matrix is used forcarrier group #A, a MIMO system that regularly hops between precodingmatrices is used for carrier group #B, only stream s1 is transmitted incarrier group #C, and space-time block coding is used to transmitcarrier group #D.

FIGS. 48A and 48B show an example according to the present embodiment offrame structure in the time and frequency domains for a signaltransmitted by a broadcast station (base station) in a system thatadopts a scheme for regularly hopping between precoding matrices using amulti-carrier transmission scheme such as OFDM. FIGS. 48A and 48B show aframe structure at a different time than FIGS. 47A and 47B, from time $Xto time $X+T′. In FIGS. 48A and 48B, as in FIGS. 47A and 47B, the(sub)carriers used when using OFDM are divided as follows: a carriergroup #A composed of (sub)carrier a−(sub)carrier a+Na, a carrier group#B composed of (sub)carrier b−(sub)carrier b+Nb, a carrier group #Ccomposed of (sub)carrier c−(sub)carrier c+Nc, a carrier group #Dcomposed of (sub)carrier d−(sub)carrier d+Nd, . . . . The differencebetween FIGS. 47A and 47B and FIGS. 48A and 48B is that in some carriergroups, the transmission scheme used in FIGS. 47A and 47B differs fromthe transmission scheme used in FIGS. 48A and 48B. In FIGS. 48A and 48B,space-time block coding is used to transmit carrier group #A, a MIMOsystem that regularly hops between precoding matrices is used forcarrier group #B, a MIMO system that regularly hops between precodingmatrices is used for carrier group #C, and only stream s1 is transmittedin carrier group #D.

Next, the supported transmission schemes are described.

FIG. 49 shows a signal processing scheme when using a spatialmultiplexing MIMO system or a MIMO system with a fixed precoding matrix.FIG. 49 bears the same numbers as in FIG. 6. A weighting unit 600, whichis a baseband signal in accordance with a certain modulation scheme,receives as inputs a stream s1(t) (307A), a stream s2(t) (307B), andinformation 315 regarding the weighting scheme, and outputs a modulatedsignal z1(t) (309A) after weighting and a modulated signal z2(t) (309B)after weighting. Here, when the information 315 regarding the weightingscheme indicates a spatial multiplexing MIMO system, the signalprocessing in scheme #1 of FIG. 49 is performed. Specifically, thefollowing processing is performed.

Math 291

$\begin{matrix}\begin{matrix}{\begin{pmatrix}{z\; 1(t)} \\{z\; 2(t)}\end{pmatrix} = {\begin{pmatrix}{\mathbb{e}}^{j\; 0} & 0 \\0 & {\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}\begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}}\end{matrix} & {{Equation}\mspace{14mu} 250}\end{matrix}$

When a scheme for transmitting one modulated signal is supported, fromthe standpoint of transmission power, Equation 250 may be represented asEquation 251.

Math 292

$\begin{matrix}\begin{matrix}{\begin{pmatrix}{z\; 1(t)} \\{z\; 2(t)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & 0 \\0 & {\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}}} \\{= {\frac{1}{\sqrt{2}}\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}\begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{\frac{1}{\sqrt{2}}s\; 1(t)} \\{\frac{1}{\sqrt{2}}s\; 2(t)}\end{pmatrix}}\end{matrix} & {{Equation}\mspace{14mu} 251}\end{matrix}$

When the information 315 regarding the weighting scheme indicates a MIMOsystem in which precoding matrices are regularly hopped between, signalprocessing in scheme #2, for example, of FIG. 49 is performed.Specifically, the following processing is performed.

Math 293

$\begin{matrix}{\begin{pmatrix}{z\; 1(t)} \\{z\; 2(t)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;\theta_{11}} & {\alpha \times {\mathbb{e}}^{j\;{({\theta_{11} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;\theta_{21}}} & {\mathbb{e}}^{j{({\theta_{21} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 252}\end{matrix}$

Here, θ₁₁, θ₁₂, λ, and δ are fixed values.

FIG. 50 shows the structure of modulated signals when using space-timeblock coding. A space-time block coding unit (5002) in FIG. 50 receives,as input, a baseband signal based on a certain modulation signal. Forexample, the space-time block coding unit (5002) receives symbol s1,symbol s2, . . . as inputs. As shown in FIG. 50, space-time block codingis performed, z1(5003A) becomes “s1 as symbol #0”, “−s2* as symbol #0”,“s3 as symbol #2”, “−s4* as symbol #3” . . . , and z2(5003B) becomes “s2as symbol #0”, “s1* as symbol #1”, “s4 as symbol #2”, “s3* as symbol #3”. . . . In this case, symbol #X in z1 and symbol #X in z2 aretransmitted from the antennas at the same time, over the same frequency.

In FIGS. 47A, 47B, 48A, and 48B, only symbols transmitting data areshown. In practice, however, it is necessary to transmit informationsuch as the transmission scheme, modulation scheme, error correctionscheme, and the like. For example, as in FIG. 51, these pieces ofinformation can be transmitted to a communication partner by regulartransmission with only one modulated signal z1. It is also necessary totransmit symbols for estimation of channel fluctuation, i.e. for thereception device to estimate channel fluctuation (for example, a pilotsymbol, reference symbol, preamble, a Phase Shift Keying (PSK) symbolknown at the transmission and reception sides, and the like). In FIGS.47A, 47B, 48A, and 48B, these symbols are omitted. In practice, however,symbols for estimating channel fluctuation are included in the framestructure in the time and frequency domains.

Accordingly, each carrier group is not composed only of symbols fortransmitting data. (The same is true for Embodiment 1 as well.) FIG. 52is an example of the structure of a transmission device in a broadcaststation (base station) according to the present embodiment. Atransmission scheme determining unit (5205) determines the number ofcarriers, modulation scheme, error correction scheme, coding rate forerror correction coding, transmission scheme, and the like for eachcarrier group and outputs a control signal (5206).

A modulated signal generating unit #1 (5201_1) receives, as input,information (5200_1) and the control signal (5206) and, based on theinformation on the transmission scheme in the control signal (5206),outputs a modulated signal z1 (5202_1) and a modulated signal z2(5203_1) in the carrier group #A of FIGS. 47A, 47B, 48A, and 48B.

Similarly, a modulated signal generating unit #2 (5201_2) receives, asinput, information (5200_2) and the control signal (5206) and, based onthe information on the transmission scheme in the control signal (5206),outputs a modulated signal z1 (5202_2) and a modulated signal z2(5203_2) in the carrier group #B of FIGS. 47A, 47B, 48A, and 48B.

Similarly, a modulated signal generating unit #3 (5201_3) receives, asinput, information (5200_3) and the control signal (5206) and, based onthe information on the transmission scheme in the control signal (5206),outputs a modulated signal z1 (5202_3) and a modulated signal z2(5203_3) in the carrier group #C of FIGS. 47A, 47B, 48A, and 48B.

Similarly, a modulated signal generating unit #4 (5201_4) receives, asinput, information (5200_4) and the control signal (5206) and, based onthe information on the transmission scheme in the control signal (5206),outputs a modulated signal z1 (5202_4) and a modulated signal z2(5203_4) in the carrier group #D of FIGS. 47A, 47B, 48A, and 48B.

While not shown in the figures, the same is true for modulated signalgenerating unit #5 through modulated signal generating unit #M−1.

Similarly, a modulated signal generating unit #M (5201_M) receives, asinput, information (5200_M) and the control signal (5206) and, based onthe information on the transmission scheme in the control signal (5206),outputs a modulated signal z1 (5202_M) and a modulated signal z2(5203_M) in a certain carrier group.

An OFDM related processor (5207_1) receives, as inputs, the modulatedsignal z1 (5202_1) in carrier group #A, the modulated signal z1 (5202_2)in carrier group #B, the modulated signal z1 (5202_3) in carrier group#C, the modulated signal z1 (5202_4) in carrier group #D, . . . , themodulated signal z1 (5202_M) in a certain carrier group #M, and thecontrol signal (5206), performs processing such as reordering, inverseFourier transform, frequency conversion, amplification, and the like,and outputs a transmission signal (5208_1). The transmission signal(5208_1) is output as a radio wave from an antenna (5209_1).

Similarly, an OFDM related processor (5207_2) receives, as inputs, themodulated signal z1 (5203_1) in carrier group #A, the modulated signalz1 (5203_2) in carrier group #B, the modulated signal z1 (5203_3) incarrier group #C, the modulated signal z1 (5203_4) in carrier group #D,. . . , the modulated signal z1 (5203_M) in a certain carrier group #M,and the control signal (5206), performs processing such as reordering,inverse Fourier transform, frequency conversion, amplification, and thelike, and outputs a transmission signal (5208_2). The transmissionsignal (5208_2) is output as a radio wave from an antenna (5209_2).

FIG. 53 shows an example of a structure of the modulated signalgenerating units #1-#M in FIG. 52. An error correction encoder (5302)receives, as inputs, information (5300) and a control signal (5301) and,in accordance with the control signal (5301), sets the error correctioncoding scheme and the coding rate for error correction coding, performserror correction coding, and outputs data (5303) after error correctioncoding. (In accordance with the setting of the error correction codingscheme and the coding rate for error correction coding, when using LDPCcoding, turbo coding, or convolutional coding, for example, depending onthe coding rate, puncturing may be performed to achieve the codingrate.)

An interleaver (5304) receives, as input, error correction coded data(5303) and the control signal (5301) and, in accordance with informationon the interleaving scheme included in the control signal (5301),reorders the error correction coded data (5303) and outputs interleaveddata (5305).

A mapping unit (5306_1) receives, as input, the interleaved data (5305)and the control signal (5301) and, in accordance with the information onthe modulation scheme included in the control signal (5301), performsmapping and outputs a baseband signal (5307_1).

Similarly, a mapping unit (5306_2) receives, as input, the interleaveddata (5305) and the control signal (5301) and, in accordance with theinformation on the modulation scheme included in the control signal(5301), performs mapping and outputs a baseband signal (5307_2).

A signal processing unit (5308) receives, as input, the baseband signal(5307_1), the baseband signal (5307_2), and the control signal (5301)and, based on information on the transmission scheme (for example, inthis embodiment, a spatial multiplexing MIMO system, a MIMO scheme usinga fixed precoding matrix, a MIMO scheme for regularly hopping betweenprecoding matrices, space-time block coding, or a transmission schemefor transmitting only stream s1) included in the control signal (5301),performs signal processing. The signal processing unit (5308) outputs aprocessed signal z1 (5309_1) and a processed signal z2 (5309_2). Notethat when the transmission scheme for transmitting only stream s1 isselected, the signal processing unit (5308) does not output theprocessed signal z2 (5309_2). Furthermore, in FIG. 53, one errorcorrection encoder is shown, but the present invention is not limited inthis way. For example, as shown in FIG. 3, a plurality of encoders maybe provided.

FIG. 54 shows an example of the structure of the OFDM related processors(5207_1 and 5207_2) in FIG. 52. Elements that operate in a similar wayto FIG. 14 bear the same reference signs. A reordering unit (5402A)receives, as input, the modulated signal z1 (5400_1) in carrier group#A, the modulated signal z1 (5400_2) in carrier group #B, the modulatedsignal z1 (5400_3) in carrier group #C, the modulated signal z1 (5400_4)in carrier group #D, . . . , the modulated signal z1 (5400_M) in acertain carrier group, and a control signal (5403), performs reordering,and output reordered signals 1405A and 1405B. Note that in FIGS. 47A,47B, 48A, 48B, and 51, an example of allocation of the carrier groups isdescribed as being formed by groups of subcarriers, but the presentinvention is not limited in this way. Carrier groups may be formed bydiscrete subcarriers at each time interval. Furthermore, in FIGS. 47A,47B, 48A, 48B, and 51, an example has been described in which the numberof carriers in each carrier group does not change over time, but thepresent invention is not limited in this way. This point will bedescribed separately below.

FIGS. 55A and 55B show an example of frame structure in the time andfrequency domains for a scheme of setting the transmission scheme foreach carrier group, as in FIGS. 47A, 47B, 48A, 48B, and 51. In FIGS. 55Aand 55B, control information symbols are labeled 5500, individualcontrol information symbols are labeled 5501, data symbols are labeled5502, and pilot symbols are labeled 5503. Furthermore, FIG. 55A showsthe frame structure in the time and frequency domains for stream s1, andFIG. 55B shows the frame structure in the time and frequency domains forstream s2.

The control information symbols are for transmitting control informationshared by the carrier group and are composed of symbols for thetransmission and reception devices to perform frequency and timesynchronization, information regarding the allocation of (sub)carriers,and the like. The control information symbols are set to be transmittedfrom only stream s1 at time $1.

The individual control information symbols are for transmitting controlinformation on individual subcarrier groups and are composed ofinformation on the transmission scheme, modulation scheme, errorcorrection coding scheme, coding rate for error correction coding, blocksize of error correction codes, and the like for the data symbols,information on the insertion scheme of pilot symbols, information on thetransmission power of pilot symbols, and the like. The individualcontrol information symbols are set to be transmitted from only streams1 at time $1.

The data symbols are for transmitting data (information), and asdescribed with reference to FIGS. 47A through 50, are symbols of one ofthe following transmission schemes, for example: a spatial multiplexingMIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO schemefor regularly hopping between precoding matrices, space-time blockcoding, or a transmission scheme for transmitting only stream s1. Notethat in carrier group #A, carrier group #B, carrier group #C, andcarrier group #D, data symbols are shown in stream s2, but when thetransmission scheme for transmitting only stream s1 is used, in somecases there are no data symbols in stream s2.

The pilot symbols are for the reception device to perform channelestimation, i.e. to estimate fluctuation corresponding to h₁₁(t),h₁₂(t), h₂₁(t), and h₂₂(t) in Equation 36. (In this embodiment, since amulti-carrier transmission scheme such as an OFDM scheme is used, thepilot symbols are for estimating fluctuation corresponding to h₁₁(t),h₁₂(t), h₂₁(t), and h₂₂(t) in each subcarrier.) Accordingly, the PSKtransmission scheme, for example, is used for the pilot symbols, whichare structured to form a pattern known by the transmission and receptiondevices. Furthermore, the reception device may use the pilot symbols forestimation of frequency offset, estimation of phase distortion, and timesynchronization.

FIG. 56 shows an example of the structure of a reception device forreceiving modulated signals transmitted by the transmission device inFIG. 52. Elements that operate in a similar way to FIG. 7 bear the samereference signs.

In FIG. 56, an OFDM related processor (5600_X) receives, as input, areceived signal 702_X, performs predetermined processing, and outputs aprocessed signal 704_X. Similarly, an OFDM related processor (5600_Y)receives, as input, a received signal 702_Y, performs predeterminedprocessing, and outputs a processed signal 704_Y.

The control information decoding unit 709 in FIG. 56 receives, as input,the processed signals 704_X and 704_Y, extracts the control informationsymbols and individual control information symbols in FIGS. 55A and 55Bto obtain the control information transmitted by these symbols, andoutputs a control signal 710 that includes the obtained information.

The channel fluctuation estimating unit 705_1 for the modulated signalz1 receives, as inputs, the processed signal 704_X and the controlsignal 710, performs channel estimation in the carrier group required bythe reception device (the desired carrier group), and outputs a channelestimation signal 706_1.

Similarly, the channel fluctuation estimating unit 705_2 for themodulated signal z2 receives, as inputs, the processed signal 704_X andthe control signal 710, performs channel estimation in the carrier grouprequired by the reception device (the desired carrier group), andoutputs a channel estimation signal 706_2.

Similarly, the channel fluctuation estimating unit 705_1 for themodulated signal z1 receives, as inputs, the processed signal 704_Y andthe control signal 710, performs channel estimation in the carrier grouprequired by the reception device (the desired carrier group), andoutputs a channel estimation signal 708_1.

Similarly, the channel fluctuation estimating unit 705_2 for themodulated signal z2 receives, as inputs, the processed signal 704_Y andthe control signal 710, performs channel estimation in the carrier grouprequired by the reception device (the desired carrier group), andoutputs a channel estimation signal 708_2.

The signal processing unit 711 receives, as inputs, the signals 706_1,706_2, 708_1, 708_2, 704_X, 704_Y, and the control signal 710. Based onthe information included in the control signal 710 on the transmissionscheme, modulation scheme, error correction coding scheme, coding ratefor error correction coding, block size of error correction codes, andthe like for the data symbols transmitted in the desired carrier group,the signal processing unit 711 demodulates and decodes the data symbolsand outputs received data 712.

FIG. 57 shows the structure of the OFDM related processors (5600_X,5600_Y) in FIG. 56. A frequency converter (5701) receives, as input, areceived signal (5700), performs frequency conversion, and outputs afrequency converted signal (5702).

A Fourier transformer (5703) receives, as input, the frequency convertedsignal (5702), performs a Fourier transform, and outputs a Fouriertransformed signal (5704).

As described above, when using a multi-carrier transmission scheme suchas an OFDM scheme, carriers are divided into a plurality of carriergroups, and the transmission scheme is set for each carrier group,thereby allowing for the reception quality and transmission speed to beset for each carrier group, which yields the advantageous effect ofconstruction of a flexible system. In this case, as described in otherembodiments, allowing for choice of a scheme of regularly hoppingbetween precoding matrices offers the advantages of obtaining highreception quality, as well as high transmission speed, in an LOSenvironment. While in the present embodiment, the transmission schemesto which a carrier group can be set are “a spatial multiplexing MIMOsystem, a MIMO scheme using a fixed precoding matrix, a MIMO scheme forregularly hopping between precoding matrices, space-time block coding,or a transmission scheme for transmitting only stream s1”, but thetransmission schemes are not limited in this way. Furthermore, thespace-time coding is not limited to the scheme described with referenceto FIG. 50, nor is the MIMO scheme using a fixed precoding matrixlimited to scheme #2 in FIG. 49, as any structure with a fixed precodingmatrix is acceptable. In the present embodiment, the case of twoantennas in the transmission device has been described, but when thenumber of antennas is larger than two as well, the same advantageouseffects may be achieved by allowing for selection of a transmissionscheme for each carrier group from among “a spatial multiplexing MIMOsystem, a MIMO scheme using a fixed precoding matrix, a MIMO scheme forregularly hopping between precoding matrices, space-time block coding,or a transmission scheme for transmitting only stream s1”.

FIGS. 58A and 58B show a scheme of allocation into carrier groups thatdiffers from FIGS. 47A, 47B, 48A, 48B, and 51. In FIGS. 47A, 47B, 48A,48B, 51, 55A, and 55B, carrier groups have described as being formed bygroups of subcarriers. In FIGS. 58A and 58B, on the other hand, thecarriers in a carrier group are arranged discretely. FIGS. 58A and 58Bshow an example of frame structure in the time and frequency domainsthat differs from FIGS. 47A, 47B, 48A, 48B, 51, 55A, and 55B. FIGS. 58Aand 58B show the frame structure for carriers 1 through H, times $1through $K. Elements that are similar to FIGS. 55A and 55B bear the samereference signs. Among the data symbols in FIGS. 58A and 58B, the “A”symbols are symbols in carrier group A, the “B” symbols are symbols incarrier group B, the “C” symbols are symbols in carrier group C, and the“D” symbols are symbols in carrier group D. The carrier groups can thusbe similarly implemented by discrete arrangement along (sub)carriers,and the same carrier need not always be used in the time domain. Thistype of arrangement yields the advantageous effect of obtaining time andfrequency diversity gain.

In FIGS. 47A, 47B, 48A, 48B, 51, 58A, and 58B, the control informationsymbols and the individual control information symbols are allocated tothe same time in each carrier group, but these symbols may be allocatedto different times. Furthermore, the number of (sub)carriers used by acarrier group may change over time.

Embodiment 16

Like Embodiment 10, the present embodiment describes a scheme forregularly hopping between precoding matrices using a unitary matrix whenN is an odd number.

In the scheme of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

Math 294

$\begin{matrix}{{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 253}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0.

Math 295

$\begin{matrix}{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{{j\theta}_{11}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 254}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. (Let the α inEquation 253 and the α in Equation 254 be the same value.)

From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment3, the following conditions are important in Equation 253 for achievingexcellent data reception quality.

Math 296

Condition #46e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

(x is 0, 1, 2, . . . , N−2,N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Math 297e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Addition of the following condition is considered.

Math 298θ₁₁(x)=θ₁₁(x+N) for ∀x(x=0,1,2, . . . ,N−2,N−1)andθ₂₁(y)=θ₂₁(y+N) for ∀y(y=0,1,2, . . . ,N−2,N−1)

Next, in order to distribute the poor reception points evenly withregards to phase in the complex plane, as described in Embodiment 6,Condition #49 and Condition #50 are provided.

Math 299

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{(\frac{2\pi}{N})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 49}}\end{matrix}$Math 300

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\pi}{N}})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 50}}\end{matrix}$

In other words, Condition #49 means that the difference in phase is 2π/Nradians. On the other hand, Condition #50 means that the difference inphase is −2π/N radians.

Letting θ₁₁(0)−θ₂₁(0)=0 radians, and letting α>1, the distribution ofpoor reception points for s1 and for s2 in the complex plane for N=3 isshown in FIGS. 60A and 60B. As is clear from FIGS. 60A and 60B, in thecomplex plane, the minimum distance between poor reception points for s1is kept large, and similarly, the minimum distance between poorreception points for s2 is also kept large. Similar conditions arecreated when α<1. Furthermore, upon comparison with FIGS. 45A and 45B inEmbodiment 10, making the same considerations as in Embodiment 9, theprobability of a greater distance between poor reception points in thecomplex plane increases when N is an odd number as compared to when N isan even number. However, when N is small, for example when N≦16, theminimum distance between poor reception points in the complex plane canbe guaranteed to be a certain length, since the number of poor receptionpoints is small. Accordingly, when N≦16, even if N is an even number,cases do exist where data reception quality can be guaranteed.

Therefore, in the scheme for regularly hopping between precodingmatrices based on Equations 253 and 254, when N is set to an odd number,the probability of improving data reception quality is high. Precodingmatrices F[0]−F[2N−1] are generated based on Equations 253 and 254 (theprecoding matrices F[0]−F[2N−1] may be in any order for the 2N slots inthe period (cycle)). Symbol number 2Ni may be precoded using F[0],symbol number 2Ni+1 may be precoded using F[1], . . . , and symbolnumber 2N×i+h may be precoded using F[h], for example (h=0, 1, 2, . . ., 2N−2, 2N−1). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.) Furthermore,when the modulation scheme for both s1 and s2 is 16QAM, if α is set asin Equation 233, the advantageous effect of increasing the minimumdistance between 16×16=256 signal points in the I-Q plane for a specificLOS environment may be achieved.

The following conditions are possible as conditions differing fromCondition #48:

Math 301

Condition #51e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . ,2N−2, 2N−1; and x≠y.)Math 302Condition #52e ^(j(θ) ¹¹ ^((x))−θ) ²¹ ^((x)−π))≠^(j(θ) ¹¹ ^((y))−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . ,2N−2, 2N−1; and x≠y.)

In this case, by satisfying Condition #46, Condition #47, Condition #51,and Condition #52, the distance in the complex plane between poorreception points for s1 is increased, as is the distance between poorreception points for s2, thereby achieving excellent data receptionquality.

In the present embodiment, the scheme of structuring 2N differentprecoding matrices for a precoding hopping scheme with a 2N-slot timeperiod (cycle) has been described. In this case, as the 2N differentprecoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] areprepared. In the present embodiment, an example of a single carriertransmission scheme has been described, and therefore the case ofarranging symbols in the order F[0], F[1], F[2], . . . , F[2N−2],F[2N−1] in the time domain (or the frequency domain) has been described.The present invention is not, however, limited in this way, and the 2Ndifferent precoding matrices F[0], F[1], F[2], . . . , F[2N−2], F[2N−1]generated in the present embodiment may be adapted to a multi-carriertransmission scheme such as an OFDM transmission scheme or the like. Asin Embodiment 1, as a scheme of adaption in this case, precoding weightsmay be changed by arranging symbols in the frequency domain and in thefrequency-time domain. Note that a precoding hopping scheme with a2N-slot time period (cycle) has been described, but the sameadvantageous effects may be obtained by randomly using 2N differentprecoding matrices. In other words, the 2N different precoding matricesdo not necessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slots2N in the period (cycle) of the above scheme of regularly hoppingbetween precoding matrices), when the 2N different precoding matrices ofthe present embodiment are included, the probability of excellentreception quality increases.

Embodiment 17

The present embodiment describes a concrete example of the scheme ofregularly changing precoding weights, based on Embodiment 8.

FIG. 6 relates to the weighting scheme (precoding scheme) in the presentembodiment. The weighting unit 600 integrates the weighting units 308Aand 308B in FIG. 3. As shown in FIG. 6, the stream s1(t) and the streams2(t) correspond to the baseband signals 307A and 307B in FIG. 3. Inother words, the streams s1(t) and s2(t) are the baseband signalin-phase components I and quadrature components Q when mapped accordingto a modulation scheme such as QPSK, 16QAM, 64QAM, or the like. Asindicated by the frame structure of FIG. 6, in the stream s1(t), asignal at symbol number u is represented as s1(u), a signal at symbolnumber u+1 as s1(u+1), and so forth. Similarly, in the stream s2(t), asignal at symbol number u is represented as s2(u), a signal at symbolnumber u+1 as s2(u+1), and so forth. The weighting unit 600 receives thebaseband signals 307A (s1(t)) and 307B (s2(t)) and the information 315regarding weighting information in FIG. 3 as inputs, performs weightingin accordance with the information 315 regarding weighting, and outputsthe signals 309A (z1(t)) and 309B (z2(t)) after weighting in FIG. 3.

At this point, when for example a precoding matrix hopping scheme withan N=8 period (cycle) as in Example #8 in Embodiment 6 is used, z1(t)and z2(t) are represented as follows. For symbol number 8i (where i isan integer greater than or equal to zero):

Math 303

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {8i} \right)} \\{z\; 2\left( {8i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {8i} \right)} \\{s\; 2\left( {8i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 255}\end{matrix}$

Here, j is an imaginary unit, and k=0.

For symbol number 8i+1:

Math 304

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 1} \right)} \\{z\; 2\left( {{8i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 1} \right)} \\{s\; 2\left( {{8i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 256}\end{matrix}$

Here, k=1.

For symbol number 8i+2:

Math 305

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 2} \right)} \\{z\; 2\left( {{8i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 2} \right)} \\{s\; 2\left( {{8i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 257}\end{matrix}$

Here, k=2.

For symbol number 8i+3:

Math 306

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 3} \right)} \\{z\; 2\left( {{8i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 3} \right)} \\{s\; 2\left( {{8i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 258}\end{matrix}$

Here, k=3.

For symbol number 8i+4:

Math 307

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 4} \right)} \\{z\; 2\left( {{8i} + 4} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 4} \right)} \\{s\; 2\left( {{8i} + 4} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 259}\end{matrix}$

Here, k=4.

For symbol number 8i+5:

Math 308

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 5} \right)} \\{z\; 2\left( {{8i} + 5} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 5} \right)} \\{s\; 2\left( {{8i} + 5} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 260}\end{matrix}$

Here, k=5.

For symbol number 8i+6:

Math 309

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 6} \right)} \\{z\; 2\left( {{8i} + 6} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 6} \right)} \\{s\; 2\left( {{8i} + 6} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 261}\end{matrix}$

Here, k=6.

For symbol number 8i+7:

Math 310

$\begin{matrix}{\begin{pmatrix}{z\; 1\left( {{8i} + 7} \right)} \\{z\; 2\left( {{8i} + 7} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 7} \right)} \\{s\; 2\left( {{8i} + 7} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 262}\end{matrix}$

Here, k=7.

The symbol numbers shown here can be considered to indicate time. Asdescribed in other embodiments, in Equation 262, for example, z1(8i+7)and z2(8i+7) at time 8i+7 are signals at the same time, and thetransmission device transmits z1(8i+7) and z2(8i+7) over the same(shared/common) frequency. In other words, letting the signals at time Tbe s1(T), s2(T), z1(T), and z2(T), then z1(T) and z2(T) are sought fromsome sort of precoding matrices and from s1(T) and s2(T), and thetransmission device transmits z1(T) and z2(T) over the same(shared/common) frequency (at the same time). Furthermore, in the caseof using a multi-carrier transmission scheme such as OFDM or the like,and letting signals corresponding to s1, s2, z1, and z2 for (sub)carrierL and time T be s1(T, L), s2(T, L), z1(T, L), and z2(T, L), then z1(T,L) and z2(T, L) are sought from some sort of precoding matrices and froms1(T, L) and s2(T, L), and the transmission device transmits z1(T, L)and z2(T, L) over the same (shared/common) frequency (at the same time).In this case, the appropriate value of α is given by Equation 198 orEquation 200. Also, different values of α may be set in Equations255-262. That is to say, when two equations (Equations X and Y) areextracted from Equations 255-262, the value of α given by Equation X maybe different from the value of α given by Equation Y.

The present embodiment describes a precoding hopping scheme thatincreases period (cycle) size, based on the above-described precodingmatrices of Equation 190.

Letting the period (cycle) of the precoding hopping scheme be 8M, 8Mdifferent precoding matrices are represented as follows.

Math 311

$\begin{matrix}{{F\left\lbrack {{8 \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{k\;\pi}{4M}})}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{k\;\pi}{4M} + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 263}\end{matrix}$

In this case, i=0, 1, 2, 3, 4, 5, 6, 7, and k=0, 1, . . . , M−2, M−1.

For example, letting M=2 and α<1, the poor reception points for s1 (◯)and for s2 (□) at k=0 are represented as in FIG. 42A. Similarly, thepoor reception points for s1 (◯) and for s2 (□) at k=1 are representedas in FIG. 42B. In this way, based on the precoding matrices in Equation190, the poor reception points are as in FIG. 42A, and by using, as theprecoding matrices, the matrices yielded by multiplying each term in thesecond line on the right-hand side of Equation 190 by e^(jX) (seeEquation 226), the poor reception points are rotated with respect toFIG. 42A (see FIG. 42B). (Note that the poor reception points in FIG.42A and FIG. 42B do not overlap. Even when multiplying by e^(jX), thepoor reception points should not overlap, as in this case. Furthermore,the matrices yielded by multiplying each term in the first line on theright-hand side of Equation 190, rather than in the second line on theright-hand side of Equation 190, by e^(jX) may be used as the precodingmatrices.) In this case, the precoding matrices F[0]−F[15] arerepresented as follows.

Math 312

$\begin{matrix}{{F\left\lbrack {{8 \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + {Xk}})}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + {Xk} + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 264}\end{matrix}$

Here, i=0, 1, 2, 3, 4, 5, 6, 7, and k=0, 1.

In this case, when M=2, precoding matrices F[0]−F[15] are generated (theprecoding matrices F[0]−F[15] may be in any order. Also, matricesF[0]−F[15] may be different matrices). Symbol number 16i may be precodedusing F[0], symbol number 16i+1 may be precoded using F[1], . . . , andsymbol number 16i+h may be precoded using F[h], for example (h=0, 1, 2,. . . , 14, 15). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.) Summarizingthe above considerations, with reference to Equations 82-85, N-period(cycle) precoding matrices are represented by the following equation.

Math 313

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 265}\end{matrix}$

Here, since the period (cycle) has N slots, i=0, 1, 2, . . . , N−2, N−1.

Furthermore, the N×M period (cycle) precoding matrices based on Equation265 are represented by the following equation.

Math 314

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + X_{k}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + X_{k} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 266}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.

In this case, precoding matrices F[0]−F[N×M−1] are generated. (Precodingmatrices F[0]−F[N×M−1] may be in any order for the N×M slots in theperiod (cycle)). Symbol number N×M×i may be precoded using F[0], symbolnumber N×M×i+1 may be precoded using F[1], . . . , and symbol numberN×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . ,N×M−2, N×M−1). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality. Note that while the N×M period(cycle) precoding matrices have been set to Equation 266, the N×M period(cycle) precoding matrices may be set to the following equation, asdescribed above.

Math 315

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j{({{\theta_{11}{(i)}} + X_{k}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + X_{k} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 267}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.

In Equations 265 and 266, when 0 radians≦δ<2π radians, the matrices area unitary matrix when δ=π radians and are a non-unitary matrix when δ≠πradians. In the present scheme, use of a non-unitary matrix for π/2radians≦|δ|<π radians is one characteristic structure (the conditionsfor δ being similar to other embodiments), and excellent data receptionquality is obtained. However, not limited to this, a unitary matrix maybe used instead.

In the present embodiment, as one example of the case where λ is treatedas a fixed value, a case where λ=0 radians is described. However, inview of the mapping according to the modulation scheme, λ may be set toa fixed value defined as λ=π/2 radians, λ=π radians, or λ=(3π)/2radians. (For example, λ may be set to a fixed value defined as λ=πradians in the precoding matrices of the precoding scheme in whichhopping between precoding matrices is performed regularly.) With thisstructure, as is the case where λ is set to a value defined as λ=0radians, a reduction in circuit size is achieved.

Embodiment 18

The present embodiment describes a scheme for regularly hopping betweenprecoding matrices using a unitary matrix based on Embodiment 9.

As described in Embodiment 8, in the scheme of regularly hopping betweenprecoding matrices over a period (cycle) with N slots, the precodingmatrices prepared for the N slots with reference to Equations 82-85 arerepresented as follows.

Math 316

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 268}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. (α>0.) Since a unitary matrixis used in the present embodiment, the precoding matrices in Equation268 may be represented as follows.

Math 317

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 269}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. (α>0.) From Condition #5(Math 106) and Condition #6 (Math 107) in Embodiment 3, the followingcondition is important for achieving excellent data reception quality.

Math 318

Condition #53e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 319Condition #54e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Embodiment 6 has described the distance between poor reception points.In order to increase the distance between poor reception points, it isimportant for the number of slots N to be an odd number three orgreater. The following explains this point.

In order to distribute the poor reception points evenly with regards tophase in the complex plane, as described in Embodiment 6, Condition #55and Condition #56 are provided.

Math 320

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{(\frac{2\pi}{N})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 55}}\end{matrix}$Math 321

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\pi}{N}})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 56}}\end{matrix}$

Letting θ₁₁(0)−θ₂₁(0)=0 radians, and letting α<1, the distribution ofpoor reception points for s1 and for s2 in the complex plane for an N=3period (cycle) is shown in FIG. 43A, and the distribution of poorreception points for s1 and for s2 in the complex plane for an N=4period (cycle) is shown in FIG. 43B. Letting θ₁₁(0)−θ₂₁(0)=0 radians,and letting α>1, the distribution of poor reception points for s1 andfor s2 in the complex plane for an N=3 period (cycle) is shown in FIG.44A, and the distribution of poor reception points for s1 and for s2 inthe complex plane for an N=4 period (cycle) is shown in FIG. 44B.

In this case, when considering the phase between a line segment from theorigin to a poor reception point and a half line along the real axisdefined by real ≧0 (see FIG. 43A), then for either α>1 or α<1, when N=4,the case always occurs wherein the phase for the poor reception pointsfor s1 and the phase for the poor reception points for s2 are the samevalue. (See 4301, 4302 in FIG. 43B, and 4401, 4402 in FIG. 44B.) In thiscase, in the complex plane, the distance between poor reception pointsbecomes small. On the other hand, when N=3, the phase for the poorreception points for s1 and the phase for the poor reception points fors2 are never the same value.

Based on the above, considering how the case always occurs wherein thephase for the poor reception points for s1 and the phase for the poorreception points for s2 are the same value when the number of slots N inthe period (cycle) is an even number, setting the number of slots N inthe period (cycle) to an odd number increases the probability of agreater distance between poor reception points in the complex plane ascompared to when the number of slots N in the period (cycle) is an evennumber. However, when the number of slots N in the period (cycle) issmall, for example when N≦16, the minimum distance between poorreception points in the complex plane can be guaranteed to be a certainlength, since the number of poor reception points is small. Accordingly,when N≦16, even if N is an even number, cases do exist where datareception quality can be guaranteed.

Therefore, in the scheme for regularly hopping between precodingmatrices based on Equation 269, when the number of slots N in the period(cycle) is set to an odd number, the probability of improving datareception quality is high. Precoding matrices F[0]−F[N−1] are generatedbased on Equation 269 (the precoding matrices F[0]−F[N−1] may be in anyorder for the N slots in the period (cycle)).

Symbol number Ni may be precoded using F[0], symbol number Ni+1 may beprecoded using F[1], . . . , and symbol number N×i+h may be precodedusing F[h], for example (h=0, 1, 2, . . . , N−2, N−1). (In this case, asdescribed in previous embodiments, precoding matrices need not be hoppedbetween regularly.) Furthermore, when the modulation scheme for both s1and s2 is 16QAM, if α is set as follows,

Math 322

$\begin{matrix}{\alpha = \frac{\sqrt{2} + 4}{\sqrt{2} + 2}} & {{Equation}\mspace{14mu} 270}\end{matrix}$the advantageous effect of increasing the minimum distance between16×16=256 signal points in the I-Q plane for a specific LOS environmentmay be achieved.

FIG. 94 shows signal point layout in the I-Q plane for 16QAM. In FIG.94, signal point 9400 is a signal point when bits to be transmitted(input bits) b0-b3 represent a value “(b0, b1, b2, b3)=(1, 0, 0, 0)” (asshown in FIG. 94), and its coordinates in the I-Q plane are (−3×g, 3×g).With regard to the signal points other than signal point 9400, the bitsto be transmitted and the coordinates in the I-Q plane can be identifiedfrom FIG. 94.

FIG. 95 shows signal point layout in the I-Q plane for QPSK. In FIG. 95,signal point 9500 is a signal point when bits to be transmitted (inputbits) b0 and b1 represent a value “(b0, b1)=(1, 0)” (as shown in FIG.95), and its coordinates in the I-Q plane are (−1×g, 1×g). With regardto the signal points other than signal point 9500, the bits to betransmitted and the coordinates in the I-Q plane can be identified fromFIG. 95.

Also, when the modulation scheme for s1 is QPSK modulation and themodulation scheme for s2 is 16QAM, if α is set as follows,

Math 323

$\begin{matrix}{\alpha = \frac{\sqrt{2} + 3 + \sqrt{5}}{\sqrt{2} + 3 - \sqrt{5}}} & {{Equation}\mspace{14mu} 271}\end{matrix}$the advantageous effect of increasing the minimum distance betweencandidate signal points in the I-Q plane for a specific LOS environmentmay be achieved.

Note that a signal point layout in the I-Q plane for 16QAM is shown inFIG. 94, and a signal point layout in the I-Q plane for QPSK is shown inFIG. 95. Here, if g in FIG. 94 is set as follows,

Math 324

$\begin{matrix}{g = \frac{z}{\sqrt{10}}} & {{Equation}\mspace{14mu} 272}\end{matrix}$h in FIG. 94 is obtained as follows.Math 325

$\begin{matrix}{h = \frac{z}{\sqrt{2}}} & {{Equation}\mspace{14mu} 273}\end{matrix}$

As an example of the precoding matrices prepared for the N slots basedon Equation 269, the following matrices are considered:

Math 326

$\begin{matrix}{{F\left\lbrack {i = 0} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\; 0}} & {\mathbb{e}}^{j\;\pi}\end{pmatrix}}} & {{Equation}\mspace{14mu} 274}\end{matrix}$Math 327

$\begin{matrix}{{F\left\lbrack {i = 1} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{2}{5}\pi}} & {\mathbb{e}}^{j{({{\frac{2}{5}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 275}\end{matrix}$Math 328

$\begin{matrix}{{F\left\lbrack {i = 2} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{4}{5}\pi}} & {\mathbb{e}}^{j{({{\frac{4}{5}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 276}\end{matrix}$Math 329

$\begin{matrix}{{F\left\lbrack {i = 3} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{6}{5}\pi}} & {\mathbb{e}}^{j{({{\frac{6}{5}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 277}\end{matrix}$Math 330

$\begin{matrix}{{F\left\lbrack {i = 4} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{8}{5}\pi}} & {\mathbb{e}}^{j{({{\frac{8}{5}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 278}\end{matrix}$

Note that, in order to restrict the calculation scale of the aboveprecoding in the transmission device, θ₁₁(i)=0 radians and λ=0 radiansmay be set in Equation 269. In this case, however, in Equation 269, λmay vary depending on i, or may be the same value. That is to say, inEquation 269, λ in F[i=x] and λF[i=y](x≠y) may be the same value or maybe different values.

As the value to which α is set, the above-described set value is one ofeffective values. However, not limited to this, α may be set, forexample, for each value of i in the precoding matrix F[i] as describedin Embodiment 17. (That is to say, in F[i], α is not necessarily bealways set to a constant value for i).

In the present embodiment, the scheme of structuring N differentprecoding matrices for a precoding hopping scheme with an N-slot timeperiod (cycle) has been described. In this case, as the N differentprecoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] areprepared. In the single carrier transmission scheme, symbols arearranged in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in thetime domain (or the frequency domain in the case of the multi-carriertransmission scheme). The present invention is not, however, limited inthis way, and the N different precoding matrices F[0], F[1], F[2], . . ., F[N−2], F[N−1] generated in the present embodiment may be adapted to amulti-carrier transmission scheme such as an OFDM transmission scheme orthe like. As in Embodiment 1, as a scheme of adaptation in this case,precoding weights may be changed by arranging symbols in the frequencydomain and in the frequency-time domain. Note that a precoding hoppingscheme with an N-slot time period (cycle) has been described, but thesame advantageous effects may be obtained by randomly using N differentprecoding matrices. In other words, the N different precoding matricesdo not necessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slotsN in the period (cycle) of the above scheme of regularly hopping betweenprecoding matrices), when the N different precoding matrices of thepresent embodiment are included, the probability of excellent receptionquality increases. In this case, Condition #55 and Condition #56 can bereplaced by the following conditions. (The number of slots in the period(cycle) is considered to be N.)

Math 331

Condition #55′e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 332Condition #56′e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

In the present embodiment, as one example of the case where λ is treatedas a fixed value, a case where λ=0 radians is described. However, inview of the mapping according to the modulation scheme, λ may be set toa fixed value defined as λ=π/2 radians, λ=17 radians, or λ=(3π)/2radians. (For example, λ may be set to a fixed value defined as λ=πradians in the precoding matrices of the precoding scheme in whichhopping between precoding matrices is performed regularly.) With thisstructure, as is the case where λ is set to a value defined as λ=0radians, a reduction in circuit size is achieved.

Embodiment 19

The present embodiment describes a scheme for regularly hopping betweenprecoding matrices using a unitary matrix based on Embodiment 10.

In the scheme of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

Math 333

$\begin{matrix}{{{{{When}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{(i)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 279}\end{matrix}$α>0, and α is a fixed value (regardless of i).Math 334

$\begin{matrix}{{{{{When}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;{\theta_{11}{(i)}}}} & {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 280}\end{matrix}$α>0, and α is a fixed value (regardless of i).(The value of α in Equation 279 is the same as the value of α inEquation 280.) (The value of α may be set as α<0.)

From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment3, the following condition is important for achieving excellent datareception quality.

Math 335

Condition #57e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 336Condition #58e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Addition of the following condition is considered.

Math 337

Condition #59θ₁₁(x)=θ₁₁(x+N) for ∀x(x=0,1,2, . . . ,N−2,N−1)andθ₂₁(y)=θ₂₁(y+N) for ∀y(y=0,1,2, . . . ,N−2,N−1)

Next, in order to distribute the poor reception points evenly withregards to phase in the complex plane, as described in Embodiment 6,Condition #60 and Condition #61 are provided.

Math 338

$\begin{matrix}{{\frac{{\mathbb{e}}^{j\;{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{(\frac{2\pi}{N})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 60}}\end{matrix}$Math 339

$\begin{matrix}{{\frac{{\mathbb{e}}^{j\;{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\pi}{N}})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 61}}\end{matrix}$

Letting θ₁₁(0)−θ₂₁(0)=0 radians, and letting α>1, the distribution ofpoor reception points for s1 and for s2 in the complex plane for N=4 isshown in FIGS. 43A and 43B. As is clear from FIGS. 43A and 43B, in thecomplex plane, the minimum distance between poor reception points for s1is kept large, and similarly, the minimum distance between poorreception points for s2 is also kept large. Similar conditions arecreated when α<1. Furthermore, making the same considerations as inEmbodiment 9, the probability of a greater distance between poorreception points in the complex plane increases when N is an odd numberas compared to when N is an even number. However, when N is small, forexample when N≦16, the minimum distance between poor reception points inthe complex plane can be guaranteed to be a certain length, since thenumber of poor reception points is small. Accordingly, when N≦16, evenif N is an even number, cases do exist where data reception quality canbe guaranteed.

Therefore, in the scheme for regularly hopping between precodingmatrices based on Equations 279 and 280, when N is set to an odd number,the probability of improving data reception quality is high. Note thatprecoding matrices F[0]−F[2N−1] have been generated based on Equations279 and 280. (The precoding matrices F[0]−F[2N−1] may be in any orderfor the 2N slots in the period (cycle)). Symbol number 2Ni may beprecoded using F[0], symbol number 2Ni+1 may be precoded using F[1], . .. , and symbol number 2N×i+h may be precoded using F[h], for example(h=0, 1, 2, . . . , 2N−2, 2N−1). (In this case, as described in previousembodiments, precoding matrices need not be hopped between regularly.)Furthermore, when the modulation scheme for both s1 and s2 is 16QAM, ifα is set as in Equation 270, the advantageous effect of increasing theminimum distance between 16×16=256 signal points in the I-Q plane for aspecific LOS environment may be achieved.

Also, when the modulation scheme for s1 is QPSK modulation and themodulation scheme for s2 is 16QAM, if α is set as in Equation 271, theadvantageous effect of increasing the minimum distance between candidatesignal points in the I-Q plane for a specific LOS environment may beachieved. Note that a signal point layout in the I-Q plane for 16QAM isshown in FIG. 60, and a signal point layout in the I-Q plane for QPSK isshown in FIG. 94. Here, if “g” in FIG. 60 is set as in Equation 272,follows, “h” in FIG. 94 is obtained as in Equation 273.

The following conditions are possible as conditions differing fromCondition #59:

Math 340

Condition #62e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)(x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . , 2N−2,2N−1; and x≠y.)Math 341Condition #63e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)(x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . , 2N−2,2N−1; and x≠y.)

In this case, by satisfying Condition #57 and Condition #58 andCondition #62 and Condition #63, the distance in the complex planebetween poor reception points for s1 is increased, as is the distancebetween poor reception points for s2, thereby achieving excellent datareception quality.

As an example of the precoding matrices prepared for the 2N slots basedon Equations 279 and 280, the following matrices are considered whenN=15:

Math 342

$\begin{matrix}{{F\left\lbrack {i = 0} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j0}} & {\mathbb{e}}^{j\pi}\end{pmatrix}}} & {{Equation}\mspace{14mu} 281}\end{matrix}$Math 343

$\begin{matrix}{{F\left\lbrack {i = 1} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{2}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{2}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 282}\end{matrix}$Math 344

$\begin{matrix}{{F\left\lbrack {i = 2} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{4}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{4}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 283}\end{matrix}$Math 345

$\begin{matrix}{{F\left\lbrack {i = 3} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{6}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{6}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 284}\end{matrix}$Math 346

$\begin{matrix}{{F\left\lbrack {i = 4} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{8}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{8}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 285}\end{matrix}$Math 347

$\begin{matrix}{{F\left\lbrack {i = 5} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{10}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{10}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 286}\end{matrix}$Math 348

$\begin{matrix}{{F\left\lbrack {i = 6} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{12}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{12}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 287}\end{matrix}$Math 349

$\begin{matrix}{{F\left\lbrack {i = 7} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times j^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{14}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{14}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 288}\end{matrix}$Math 350

$\begin{matrix}{{F\left\lbrack {i = 8} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times j^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{16}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{16}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 289}\end{matrix}$Math 351

$\begin{matrix}{{F\left\lbrack {i = 9} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times j^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{18}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{18}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 290}\end{matrix}$Math 352

$\begin{matrix}{{F\left\lbrack {i = 10} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times j^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{20}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{20}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 291}\end{matrix}$Math 353

$\begin{matrix}{{F\left\lbrack {i = 11} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{22}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{22}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 292}\end{matrix}$Math 354

$\begin{matrix}{{F\left\lbrack {i = 12} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{24}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{24}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 293}\end{matrix}$Math 355

$\begin{matrix}{{F\left\lbrack {i = 13} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{26}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{26}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 294}\end{matrix}$Math 356

$\begin{matrix}{{F\left\lbrack {i = 14} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{28}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{28}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 295}\end{matrix}$Math 357

$\begin{matrix}{{F\left\lbrack {i = 15} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\; 0}} & {\mathbb{e}}^{j\;\pi} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 296}\end{matrix}$Math 358

$\begin{matrix}{{F\left\lbrack {i = 16} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{2}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{2}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 297}\end{matrix}$Math 359

$\begin{matrix}{{F\left\lbrack {i = 17} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{4}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{4}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 298}\end{matrix}$Math 360

$\begin{matrix}{{F\left\lbrack {i = 18} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{6}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{6}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 299}\end{matrix}$Math 361

$\begin{matrix}{{F\left\lbrack {i = 19} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{8}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{8}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 300}\end{matrix}$Math 362

$\begin{matrix}{{F\left\lbrack {i = 20} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{10}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{10}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 301}\end{matrix}$Math 363

$\begin{matrix}{{F\left\lbrack {i = 21} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{12}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{12}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 302}\end{matrix}$Math 364

$\begin{matrix}{{F\left\lbrack {i = 22} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{14}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{14}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 303}\end{matrix}$Math 365

$\begin{matrix}{{F\left\lbrack {i = 23} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{16}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{16}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 304}\end{matrix}$Math 366

$\begin{matrix}{{F\left\lbrack {i = 24} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{18}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{18}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 305}\end{matrix}$Math 367

$\begin{matrix}{{F\left\lbrack {i = 25} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{20}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{20}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 306}\end{matrix}$Math 368

$\begin{matrix}{{F\left\lbrack {i = 26} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{22}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{22}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 307}\end{matrix}$Math 369

$\begin{matrix}{{F\left\lbrack {i = 27} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{24}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{24}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 308}\end{matrix}$Math 370

$\begin{matrix}{{F\left\lbrack {i = 28} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{26}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{26}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 309}\end{matrix}$Math 371

$\begin{matrix}{{F\left\lbrack {i = 29} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{28}{15}}} & {\mathbb{e}}^{j{({{\frac{28}{15}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 310}\end{matrix}$

Note that, in order to restrict the calculation scale of the aboveprecoding in the transmission device, θ₁₁(i)=0 radians and λ=0 radiansmay be set in Equation 279, and θ21(i)=0 radians and λ=0 radians may beset in Equation 280.

In this case, however, in Equations 279 and 280, λ may be set as a valuethat varies depending on i, or may be set as the same value. That is tosay, in Equations 279 and 280, λ in F[i=x] and λ in F[i=y](x≠y) may bethe same value or may be different values. As another scheme, λ is setas a fixed value in Equation 279, λ is set as a fixed value in Equation280, and the fixed values of λ in Equations 279 and 280 are set asdifferent values. (As still another scheme, the fixed values of λ inEquations 279 and 280 are used.)

As the value to which α is set, the above-described set value is one ofeffective values. However, not limited to this, α may be set, forexample, for each value of i in the precoding matrix F[i] as describedin Embodiment 17. (That is to say, in F[i], α is not necessarily bealways set to a constant value for i.)

In the present embodiment, the scheme of structuring 2N differentprecoding matrices for a precoding hopping scheme with a 2N-slot timeperiod (cycle) has been described. In this case, as the 2N differentprecoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] areprepared. In the single carrier transmission scheme, symbols arearranged in the order F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] in thetime domain (or the frequency domain in the case of the multi-carriertransmission scheme). The present invention is not, however, limited inthis way, and the 2N different precoding matrices F[0], F[1], F[2], . .. , F[2N−2], F[2N−1] generated in the present embodiment may be adaptedto a multi-carrier transmission scheme such as an OFDM transmissionscheme or the like. As in Embodiment 1, as a scheme of adaptation inthis case, precoding weights may be changed by arranging symbols in thefrequency domain and in the frequency-time domain. Note that a precodinghopping scheme with a 2N-slot time period (cycle) has been described,but the same advantageous effects may be obtained by randomly using 2Ndifferent precoding matrices. In other words, the 2N different precodingmatrices do not necessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slots2N in the period (cycle) of the above scheme of regularly hoppingbetween precoding matrices), when the 2N different precoding matrices ofthe present embodiment are included, the probability of excellentreception quality increases.

In the present embodiment, as one example of the case where λ is treatedas a fixed value, a case where λ=0 radians is described. However, inview of the mapping according to the modulation scheme, λ may be set toa fixed value defined as λ=π/2 radians, λ=π radians, or λ=(3π)/2radians. (For example, λ may be set to a fixed value defined as λ=πradians in the precoding matrices of the precoding scheme in whichhopping between precoding matrices is performed regularly.) With thisstructure, as is the case where λ is set to a value defined as λ=0radians, a reduction in circuit size is achieved.

Embodiment 20

The present embodiment describes a scheme for regularly hopping betweenprecoding matrices using a unitary matrix based on Embodiment 13.

In the scheme of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

Math 372

$\begin{matrix}{{{{{When}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{{j{({{\theta_{21}{(i)}} + \lambda + \delta})}}\;}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 311}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0.

Math 373

$\begin{matrix}{{{{{When}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} & {\mathbb{e}}^{{j\theta}_{11}{(i)}} \\{\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}} & {\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 312}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. (The value of αmay be set as α<0.)

Furthermore, the 2×N×M period (cycle) precoding matrices based onEquations 311 and 312 are represented by the following equations.

Math 374

$\begin{matrix}{\mspace{20mu}{{{{{When}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + X_{k}})}}} & {{\mathbb{e}}^{j{({{\theta_{21}{(i)}} + X_{k} + \lambda + \delta})}}\;}\end{pmatrix}}}}} & {{Equation}\mspace{14mu} 313}\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

Math 375

$\begin{matrix}{\mspace{20mu}{{{{{When}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} & {\mathbb{e}}^{{j\theta}_{11}{(i)}} \\{\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta + Y_{k}})}} & {{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({i + Y_{k}})}}}\;}\end{pmatrix}}}}} & {{Equation}\mspace{14mu} 313}\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1. Furthermore, Xk=Yk may be true,or Xk≠Yk may be true.

In this case, precoding matrices F[0]−F[2N×M−1] are generated.(Precoding matrices F[0]−F[2×N×M−1] may be in any order for the 2×N×Mslots in the period (cycle)). Symbol number 2×N×M×i may be precodedusing F[0], symbol number 2×N×M×i+1 may be precoded using F[1], . . . ,and symbol number 2×N×M×i+h may be precoded using F[h], for example(h=0, 1, 2, . . . , 2×N×M−2, 2×N×M−1). (In this case, as described inprevious embodiments, precoding matrices need not be hopped betweenregularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality.

The 2×N×M period (cycle) precoding matrices in Equation 313 may bechanged to the following equation.

Math 376

$\begin{matrix}{\mspace{20mu}{{{{{When}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} & {\mathbb{e}}^{{j\theta}_{11}{(i)}} \\{\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta + Y_{k}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + Y_{k}})}}}\end{pmatrix}}}}} & {{Equation}\mspace{14mu} 315}\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

The 2×N×M period (cycle) precoding matrices in Equation 314 may also bechanged to any of Equations 316-318.

Math 377

$\begin{matrix}{\mspace{20mu}{{{{{When}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda + Y_{k}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + Y_{k}})}} \\{\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \delta})}} & {\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}}\end{pmatrix}}}}} & {{Equation}\mspace{14mu} 316}\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

Math 378

$\begin{matrix}{\mspace{20mu}{{{{{When}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{{j\theta}_{11}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{21}{(i)}} + Y_{k}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda - \delta + Y_{k}})}}}\end{pmatrix}}}}} & {{Equation}\mspace{14mu} 317}\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

Math 379

$\begin{matrix}{\mspace{79mu}{{{{When}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}} & {{Equation}\mspace{14mu} 318} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + Y_{k}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda + Y_{k}})}} \\{\mathbb{e}}^{j\;{\theta_{21}{(i)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda - \delta})}}}\end{pmatrix}}} & \;\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

Focusing on poor reception points, if Equations 313 through 318 satisfythe following conditions,

Math 380

Condition #64e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 381Condition #65e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−δ)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−δ)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 382Condition #66θ₁₁(x)=θ₁₁(x+N) for ∀x(x=0,1,2, . . . ,N−2,N−1)andθ₂₁(y)=θ₂₁(y+N) for ∀y(y=0,1,2, . . . ,N−2,N−1)then excellent data reception quality is achieved. Note that inEmbodiment 8, Condition #39 and Condition #40 should be satisfied.

Focusing on Xk and Yk, if Equations 313 through 318 satisfy thefollowing conditions,

Math 383

Condition #67X _(a) ≠X _(b)+2×s×π for ∀a,∀b(a≠b;a,b=0,1,2, . . . ,M−2,M−1)(a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1; anda≠b.)(Here, s is an integer.)Math 384Condition #68Y _(a) ≠Y _(b)+2×u×π for ∀a,∀b(a≠b;a,b=0,1,2, . . . ,M−2,M−1)(a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1; anda≠b.) (Here, u is an integer.),then excellent data reception quality is achieved. Note that inEmbodiment 8, Condition #42 should be satisfied. In Equations 313 and318, when 0 radians≦δ<2π radians, the matrices are a unitary matrix whenδ=π radians and are a non-unitary matrix when δ≠π radians. In thepresent scheme, use of a non-unitary matrix for π/2 radians≦|δ|<πradians is one characteristic structure, and excellent data receptionquality is obtained, but use of a unitary matrix is also possible.

The following provides an example of precoding matrices in the precodinghopping scheme of the present embodiment. The following matrices areconsidered when N=5, M=2 as an example of the 2×N×M period (cycle)precoding matrices based on Equations 313 through 318:

Math 385

$\begin{matrix}{{F\left\lbrack {i = 0} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\; 0}} & {\mathbb{e}}^{j\;\pi}\end{pmatrix}}} & {{Equation}\mspace{14mu} 319}\end{matrix}$Math 386

$\begin{matrix}{{F\left\lbrack {i = 1} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({\frac{2}{5}\pi})}}} & {\mathbb{e}}^{j{({{\frac{2}{5}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 320}\end{matrix}$Math 387

$\begin{matrix}{{F\left\lbrack {i = 2} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({\frac{4}{5}\pi})}}} & {\mathbb{e}}^{j{({{\frac{4}{5}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 321}\end{matrix}$Math 388

$\begin{matrix}{{F\left\lbrack {i = 3} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({\frac{6}{5}\pi})}}} & {\mathbb{e}}^{j{({{\frac{6}{5}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 322}\end{matrix}$Math 389

$\begin{matrix}{{F\left\lbrack {i = 4} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({\frac{8}{5}\pi})}}} & {\mathbb{e}}^{j{({{\frac{8}{5}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 323}\end{matrix}$Math 390

$\begin{matrix}{{F\left\lbrack {i = 5} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\; 0}} & {\mathbb{e}}^{j\;\pi} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 324}\end{matrix}$Math 391

$\begin{matrix}{{F\left\lbrack {i = 6} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{2}{5}\pi}} & {\mathbb{e}}^{j{({{\frac{2}{5}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 325}\end{matrix}$Math 392

$\begin{matrix}{{F\left\lbrack {i = 7} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{4}{5}\pi}} & {\mathbb{e}}^{j{({{\frac{4}{5}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 326}\end{matrix}$Math 393

$\begin{matrix}{{F\left\lbrack {i = 8} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{6}{5}\pi}} & {\mathbb{e}}^{j{({{\frac{6}{5}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 327}\end{matrix}$Math 394

$\begin{matrix}{{F\left\lbrack {i = 9} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{8}{5}\pi}} & {\mathbb{e}}^{j{({{\frac{8}{5}\pi} + \pi})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 328}\end{matrix}$Math 395

$\begin{matrix}{{F\left\lbrack {i = 10} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;{({0 + \pi})}}} & {\mathbb{e}}^{j\;{({\pi + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 329}\end{matrix}$Math 396

$\begin{matrix}{{F\left\lbrack {i = 11} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({{\frac{2}{5}\pi} + \pi})}}} & {\mathbb{e}}^{j{({{\frac{2}{5}\pi} + \pi + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 330}\end{matrix}$Math 397

$\begin{matrix}{{F\left\lbrack {i = 12} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({{\frac{4}{5}\pi} + \pi})}}} & {\mathbb{e}}^{j{({{\frac{4}{5}\pi} + \pi + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 331}\end{matrix}$Math 398

$\begin{matrix}{{F\left\lbrack {i = 13} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({{\frac{6}{5}\pi} + \pi})}}} & {\mathbb{e}}^{j{({{\frac{6}{5}\pi} + \pi + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 332}\end{matrix}$Math 399

$\begin{matrix}{{F\left\lbrack {i = 14} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({{\frac{8}{5}\pi} + \pi})}}} & {\mathbb{e}}^{j{({{\frac{8}{5}\pi} + \pi + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 333}\end{matrix}$Math 400

$\begin{matrix}{{F\left\lbrack {i = 15} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\; 0}} & {\mathbb{e}}^{j\;\pi} \\{\mathbb{e}}^{j{({0 + \pi})}} & {\alpha \times {\mathbb{e}}^{j{({0 + \pi})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 334}\end{matrix}$Math 401

$\begin{matrix}{{F\left\lbrack {i = 16} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{2}{5}\pi}} & {\mathbb{e}}^{j\;{({{\frac{2}{5}\pi} + \pi})}} \\{\mathbb{e}}^{j{({0 + \pi})}} & {\alpha \times {\mathbb{e}}^{j{({0 + \pi})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 335}\end{matrix}$Math 402

$\begin{matrix}{{F\left\lbrack {i = 17} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{4}{5}\pi}} & {\mathbb{e}}^{j\;{({{\frac{4}{5}\pi} + \pi})}} \\{\mathbb{e}}^{j{({0 + \pi})}} & {\alpha \times {\mathbb{e}}^{j{({0 + \pi})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 336}\end{matrix}$Math 403

$\begin{matrix}{{F\left\lbrack {i = 18} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{6}{5}\pi}} & {\mathbb{e}}^{j\;{({{\frac{6}{5}\pi} + \pi})}} \\{\mathbb{e}}^{j{({0 + \pi})}} & {\alpha \times {\mathbb{e}}^{j{({0 + \pi})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 337}\end{matrix}$Math 404

$\begin{matrix}{{F\left\lbrack {i = 19} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;\frac{8}{5}\pi}} & {\mathbb{e}}^{j\;{({{\frac{8}{5}\pi} + \pi})}} \\{\mathbb{e}}^{j{({0 + \pi})}} & {\alpha \times {\mathbb{e}}^{j{({0 + \pi})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 338}\end{matrix}$

In this way, in the above example, in order to restrict the calculationscale of the above precoding in the transmission device, λ=0 radians,δ=π radians, X1=0 radians, and X2=π radians are set in Equation 313, andλ=0 radians, δ=π radians, Y1=0 radians, and Y2=π radians are set inEquation 314. In this case, however, in Equations 313 and 314, λ may beset as a value that varies depending on i, or may be set as the samevalue. That is to say, in Equations 313 and 314, λ in F[i=x] and λ inF[i=y](x≠y) may be the same value or may be different values. As anotherscheme, λ is set as a fixed value in Equation 313, λ is set as a fixedvalue in Equation 314, and the fixed values of λ in Equations 313 and314 are set as different values. (As still another scheme, the fixedvalues of λ in Equations 313 and 314 are used.)

As the value to which α is set, the set value described in Embodiment 18is one of effective values. However, not limited to this, α may be set,for example, for each value of i in the precoding matrix F[i] asdescribed in Embodiment 17. (That is to say, in F[i], α is notnecessarily be always set to a constant value for i.)

In the present embodiment, as one example of the case where λ is treatedas a fixed value, a case where λ=0 radians is described. However, inview of the mapping according to the modulation scheme, λ may be set toa fixed value defined as λ=π/2 radians, λ=π radians, or λ=(3π)/2radians. (For example, λ may be set to a fixed value defined as λ=πradians in the precoding matrices of the precoding scheme in whichhopping between precoding matrices is performed regularly.) With thisstructure, as is the case where λ is set to a value defined as λ=0radians, a reduction in circuit size is achieved.

Embodiment 21

The present embodiment describes an example of the precoding scheme ofEmbodiment 18 in which hopping between precoding matrices is performedregularly.

As an example of the precoding matrices prepared for the N slots basedon Equation 269, the following matrices are considered:

Math 405

$\begin{matrix}{{F\left\lbrack {i = 0} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j0}} & {\mathbb{e}}^{j\pi}\end{pmatrix}}} & {{Equation}\mspace{14mu} 339}\end{matrix}$Math 406

$\begin{matrix}{{F\left\lbrack {i = 1} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{2}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{2}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 340}\end{matrix}$Math 407

$\begin{matrix}{{F\left\lbrack {i = 2} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{4}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{4}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 341}\end{matrix}$Math 408

$\begin{matrix}{{F\left\lbrack {i = 3} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{6}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{6}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 342}\end{matrix}$Math 409

$\begin{matrix}{{F\left\lbrack {i = 4} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{8}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{8}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 343}\end{matrix}$Math 410

$\begin{matrix}{{F\left\lbrack {i = 5} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{10}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{10}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 344}\end{matrix}$Math 411

$\begin{matrix}{{F\left\lbrack {i = 6} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{12}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{12}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 345}\end{matrix}$Math 412

$\begin{matrix}{{F\left\lbrack {i = 7} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{14}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{14}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 346}\end{matrix}$Math 413

$\begin{matrix}{{F\left\lbrack {i = 8} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{16}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{16}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 347}\end{matrix}$

In the above equations, there is a special case where α can be set to 1.In this case, Equations 339 through 347 are represented as follows.

Math 414

$\begin{matrix}{{F\left\lbrack {i = 0} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j0} & {\mathbb{e}}^{j\;\pi}\end{pmatrix}}} & {{Equation}\mspace{14mu} 348}\end{matrix}$Math 415

$\begin{matrix}{{F\left\lbrack {i = 1} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{2}{9}\pi} & {\mathbb{e}}^{j\;{({{\frac{2}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 349}\end{matrix}$Math 416

$\begin{matrix}{{F\left\lbrack {i = 2} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{4}{9}\pi} & {\mathbb{e}}^{j\;{({{\frac{4}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 350}\end{matrix}$Math 417

$\begin{matrix}{{F\left\lbrack {i = 3} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{6}{9}\pi} & {\mathbb{e}}^{j\;{({{\frac{6}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 351}\end{matrix}$Math 418

$\begin{matrix}{{F\left\lbrack {i = 4} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{8}{9}\pi} & {\mathbb{e}}^{j\;{({{\frac{8}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 352}\end{matrix}$Math 419

$\begin{matrix}{{F\left\lbrack {i = 5} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{10}{9}\pi} & {\mathbb{e}}^{j\;{({{\frac{10}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 353}\end{matrix}$Math 420

$\begin{matrix}{{F\left\lbrack {i = 6} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{12}{9}\pi} & {\mathbb{e}}^{j\;{({{\frac{12}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 354}\end{matrix}$Math 421

$\begin{matrix}{{F\left\lbrack {i = 7} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{14}{9}\pi} & {\mathbb{e}}^{j\;{({{\frac{14}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 355}\end{matrix}$Math 422

$\begin{matrix}{{F\left\lbrack {i = 8} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{16}{9}\pi} & {\mathbb{e}}^{j\;{({{\frac{16}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 356}\end{matrix}$

As another example, as an example of the precoding matrices prepared forthe N slots based on Equation 269, the following matrices are consideredwhen N=15:

Math 423

$\begin{matrix}{{F\left\lbrack {i = 0} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j0}} & {\mathbb{e}}^{j\pi}\end{pmatrix}}} & {{Equation}\mspace{14mu} 357}\end{matrix}$Math 424

$\begin{matrix}{{F\left\lbrack {i = 1} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{2}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{2}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 358}\end{matrix}$Math 425

$\begin{matrix}{{F\left\lbrack {i = 2} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{4}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{4}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 359}\end{matrix}$Math 426

$\begin{matrix}{{F\left\lbrack {i = 3} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{6}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{6}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 360}\end{matrix}$Math 427

$\begin{matrix}{{F\left\lbrack {i = 4} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{8}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{8}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 361}\end{matrix}$Math 428

$\begin{matrix}{{F\left\lbrack {i = 5} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{10}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{10}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 362}\end{matrix}$Math 429

$\begin{matrix}{{F\left\lbrack {i = 6} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{12}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{12}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 363}\end{matrix}$Math 430

$\begin{matrix}{{F\left\lbrack {i = 7} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{14}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{14}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 364}\end{matrix}$Math 431

$\begin{matrix}{{F\left\lbrack {i = 8} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{16}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{16}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 365}\end{matrix}$Math 432

$\begin{matrix}{{F\left\lbrack {i = 9} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{18}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{18}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 366}\end{matrix}$Math 433

$\begin{matrix}{{F\left\lbrack {i = 10} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{20}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{20}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 367}\end{matrix}$Math 434

$\begin{matrix}{{F\left\lbrack {i = 11} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{22}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{22}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 368}\end{matrix}$Math 435

$\begin{matrix}{{F\left\lbrack {i = 12} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{24}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{24}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 369}\end{matrix}$Math 436

$\begin{matrix}{{F\left\lbrack {i = 13} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{26}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{26}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 370}\end{matrix}$Math 437

$\begin{matrix}{{F\left\lbrack {i = 14} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{28}{15}\pi}} & {\mathbb{e}}^{j{({{\frac{28}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 371}\end{matrix}$

In the above equations, there is a special case where α can be set to 1.In this case, Equations 357 through 371 are represented as follows.

Math 438

$\begin{matrix}{{F\left\lbrack {i = 0} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\;\pi}\end{pmatrix}}} & {{Equation}\mspace{14mu} 372}\end{matrix}$Math 439

$\begin{matrix}{{F\left\lbrack {i = 1} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\;\frac{2}{15}\pi} & {\mathbb{e}}^{j{({{\frac{2}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 373}\end{matrix}$Math 440

$\begin{matrix}{{F\left\lbrack {i = 2} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\;\frac{4}{15}\pi} & {\mathbb{e}}^{j{({{\frac{4}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 374}\end{matrix}$Math 441

$\begin{matrix}{{F\left\lbrack {i = 3} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\;\frac{6}{15}\pi} & {\mathbb{e}}^{j{({{\frac{6}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 375}\end{matrix}$Math 442

$\begin{matrix}{{F\left\lbrack {i = 4} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\;\frac{8}{15}\pi} & {\mathbb{e}}^{j{({{\frac{8}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 376}\end{matrix}$Math 443

$\begin{matrix}{{F\left\lbrack {i = 5} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\;\frac{10}{15}\pi} & {\mathbb{e}}^{j{({{\frac{10}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 377}\end{matrix}$Math 444

$\begin{matrix}{{F\left\lbrack {i = 6} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{12}{15}\pi} & {\mathbb{e}}^{j{({{\frac{12}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 378}\end{matrix}$Math 445

$\begin{matrix}{{F\left\lbrack {i = 7} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{14}{15}\pi} & {\mathbb{e}}^{j{({{\frac{14}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 379}\end{matrix}$Math 446

$\begin{matrix}{{F\left\lbrack {i = 8} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{16}{15}\pi} & {\mathbb{e}}^{j{({{\frac{16}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 380}\end{matrix}$Math 447

$\begin{matrix}{{F\left\lbrack {i = 9} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{18}{15}\pi} & {\mathbb{e}}^{j{({{\frac{18}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 381}\end{matrix}$Math 448

$\begin{matrix}{{F\left\lbrack {i = 10} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{20}{15}\pi} & {\mathbb{e}}^{j{({{\frac{20}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 382}\end{matrix}$Math 449

$\begin{matrix}{{F\left\lbrack {i = 11} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{22}{15}\pi} & {\mathbb{e}}^{j{({{\frac{22}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 383}\end{matrix}$Math 450

$\begin{matrix}{{F\left\lbrack {i = 12} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{24}{9}\pi} & {\mathbb{e}}^{j{({{\frac{24}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 384}\end{matrix}$Math 451

$\begin{matrix}{{F\left\lbrack {i = 13} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{26}{15}\pi} & {\mathbb{e}}^{j{({{\frac{26}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 385}\end{matrix}$Math 452

$\begin{matrix}{{F\left\lbrack {i = 14} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{28}{15}\pi} & {\mathbb{e}}^{j{({{\frac{28}{15}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 386}\end{matrix}$

In the present example, α is set to 1. However, the value to which α isset is not limited to this. For example, the set value of α may beapplied to the following case. That is to say, as shown in FIG. 3 or thelike, the encoder performs an error correction coding. The value of αmay be varied depending on the coding rate for error correction codingused in the error correction coding. For example, there is considered ascheme in which α is set to 1 when the coding rate is ½, and to a valueother than 1 such as a value satisfying the relationship α>1 (or α<1)when the coding rate is ⅔. With this structure, in the reception device,excellent data reception quality may be achieved regardless of thecoding rate. (Excellent data reception quality may be achieved even if αis set as a fixed value.)

As another example, as described in Embodiment 17, α may be set for eachvalue of i in the precoding matrix F[i]. (That is to say, in F[i], α isnot necessarily be always set to a constant value for i.)

In the present embodiment, the scheme of structuring N differentprecoding matrices for a precoding hopping scheme with an N-slot timeperiod (cycle) has been described. In this case, as the N differentprecoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] areprepared. In the single carrier transmission scheme, symbols arearranged in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in thetime domain (or the frequency domain in the case of the multi-carriertransmission scheme). The present invention is not, however, limited inthis way, and the N different precoding matrices F[0], F[1], F[2], . . ., F[N−2], F[N−1] generated in the present embodiment may be adapted to amulti-carrier transmission scheme such as an OFDM transmission scheme orthe like. As in Embodiment 1, as a scheme of adaptation in this case,precoding weights may be changed by arranging symbols in the frequencydomain and in the frequency-time domain. Note that a precoding hoppingscheme with an N-slot time period (cycle) has been described, but thesame advantageous effects may be obtained by randomly using N differentprecoding matrices. In other words, the N different precoding matricesdo not necessarily need to be used in a regular period (cycle).

Embodiment 22

The present embodiment describes an example of the precoding scheme ofEmbodiment 19 in which hopping between precoding matrices is performedregularly.

As an example of the precoding matrices prepared for the 2N slots basedon Equations 279 and 280, the following matrices are considered whenN=9:

Math 453

$\begin{matrix}{{F\left\lbrack {i = 0} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j0}} & {\mathbb{e}}^{j\pi}\end{pmatrix}}} & {{Equation}\mspace{14mu} 387}\end{matrix}$Math 454

$\begin{matrix}{{F\left\lbrack {i = 1} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{2}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{2}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 388}\end{matrix}$Math 455

$\begin{matrix}{{F\left\lbrack {i = 2} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{4}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{4}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 389}\end{matrix}$Math 456

$\begin{matrix}{{F\left\lbrack {i = 3} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{6}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{6}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 390}\end{matrix}$Math 457

$\begin{matrix}{{F\left\lbrack {i = 4} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{8}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{8}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 391}\end{matrix}$Math 458

$\begin{matrix}{{F\left\lbrack {i = 5} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{10}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{10}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 392}\end{matrix}$Math 459

$\begin{matrix}{{F\left\lbrack {i = 6} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{12}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{12}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 393}\end{matrix}$Math 460

$\begin{matrix}{{F\left\lbrack {i = 7} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{14}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{14}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 394}\end{matrix}$Math 461

$\begin{matrix}{{F\left\lbrack {i = 8} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{16}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{16}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 395}\end{matrix}$Math 462

$\begin{matrix}{{F\left\lbrack {i = 9} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j0}} & {\mathbb{e}}^{j\pi} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 396}\end{matrix}$Math 463

$\begin{matrix}{{F\left\lbrack {i = 10} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{2}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{2}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 397}\end{matrix}$Math 464

$\begin{matrix}{{F\left\lbrack {i = 11} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{4}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{4}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 398}\end{matrix}$Math 465

$\begin{matrix}{{F\left\lbrack {i = 12} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{6}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{6}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 399}\end{matrix}$Math 466

$\begin{matrix}{{F\left\lbrack {i = 13} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{8}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{8}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 400}\end{matrix}$Math 467

$\begin{matrix}{{F\left\lbrack {i = 14} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{10}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{10}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 401}\end{matrix}$Math 468

$\begin{matrix}{{F\left\lbrack {i = 15} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{12}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{12}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 402}\end{matrix}$Math 469

$\begin{matrix}{{F\left\lbrack {i = 16} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{14}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{14}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 403}\end{matrix}$Math 470

$\begin{matrix}{{F\left\lbrack {i = 17} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{16}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{16}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 404}\end{matrix}$

In the above equations, there is a special case where α can be set to 1.In this case, Equations 387 through 404 are represented as follows.

Math 471

$\begin{matrix}{{F\left\lbrack {i = 0} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j0}} & {\mathbb{e}}^{j\pi}\end{pmatrix}}} & {{Equation}\mspace{14mu} 405}\end{matrix}$Math 472

$\begin{matrix}{{F\left\lbrack {i = 1} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{2}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{2}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 406}\end{matrix}$Math 473

$\begin{matrix}{{F\left\lbrack {i = 2} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{4}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{4}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 407}\end{matrix}$Math 474

$\begin{matrix}{{F\left\lbrack {i = 3} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{6}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{6}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 408}\end{matrix}$Math 475

$\begin{matrix}{{F\left\lbrack {i = 4} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{8}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{8}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 409}\end{matrix}$Math 476

$\begin{matrix}{{F\left\lbrack {i = 5} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{10}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{10}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 410}\end{matrix}$Math 477

$\begin{matrix}{{F\left\lbrack {i = 6} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{12}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{12}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 411}\end{matrix}$Math 478

$\begin{matrix}{{F\left\lbrack {i = 7} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{14}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{14}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 412}\end{matrix}$Math 479

$\begin{matrix}{{F\left\lbrack {i = 8} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{16}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{16}{9}\pi} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 413}\end{matrix}$Math 480

$\begin{matrix}{{F\left\lbrack {i = 9} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j0}} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 414}\end{matrix}$Math 481

$\begin{matrix}{{F\left\lbrack {i = 10} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{2}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{2}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 415}\end{matrix}$Math 482

$\begin{matrix}{{F\left\lbrack {i = 11} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{4}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{4}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 416}\end{matrix}$Math 483

$\begin{matrix}{{F\left\lbrack {i = 12} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{6}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{6}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 417}\end{matrix}$Math 484

$\begin{matrix}{{F\left\lbrack {i = 13} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{8}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{8}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 418}\end{matrix}$Math 485

$\begin{matrix}{{F\left\lbrack {i = 14} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{10}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{10}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 419}\end{matrix}$Math 486

$\begin{matrix}{{F\left\lbrack {i = 15} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{12}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{12}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 420}\end{matrix}$Math 487

$\begin{matrix}{{F\left\lbrack {i = 16} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{14}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{14}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 421}\end{matrix}$Math 488

$\begin{matrix}{{F\left\lbrack {i = 17} \right\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{16}{9}\pi}} & {\mathbb{e}}^{j{({{\frac{16}{9}\pi} + \pi})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 422}\end{matrix}$

Also, α may be set to 1 in Equations 281 through 310 presented inEmbodiment 19. As the value to which α is set, the above-described setvalue is one of effective values. However, not limited to this, α may beset, for example, for each value of i in the precoding matrix F[i] asdescribed in Embodiment 17. (That is to say, in F[i], α is notnecessarily be always set to a constant value for i.)

In the present embodiment, the scheme of structuring 2N differentprecoding matrices for a precoding hopping scheme with a 2N-slot timeperiod (cycle) has been described. In this case, as the 2N differentprecoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] areprepared. In the single carrier transmission scheme, symbols arearranged in the order F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] in thetime domain (or the frequency domain in the case of the multi-carriertransmission scheme). The present invention is not, however, limited inthis way, and the 2N different precoding matrices F[0], F[1], F[2], . .. , F[2N−2], F[2N−1] generated in the present embodiment may be adaptedto a multi-carrier transmission scheme such as an OFDM transmissionscheme or the like. As in Embodiment 1, as a scheme of adaptation inthis case, precoding weights may be changed by arranging symbols in thefrequency domain and in the frequency-time domain. Note that a precodinghopping scheme with a 2N-slot time period (cycle) has been described,but the same advantageous effects may be obtained by randomly using 2Ndifferent precoding matrices. In other words, the 2N different precodingmatrices do not necessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slots2N in the period (cycle) of the above scheme of regularly hoppingbetween precoding matrices), when the 2N different precoding matrices ofthe present embodiment are included, the probability of excellentreception quality increases.

Embodiment 23

In Embodiment 9, a scheme for regularly hopping between precodingmatrices with use of a unitary matrix has been described. In the presentembodiment, a scheme for regularly hopping between precoding matriceswith use of a matrix different from that in Embodiment 9 is described.

First, a precoding matrix F, a basic precoding matrix, is expressed bythe following equation.

Math 489

$\begin{matrix}{F = \begin{pmatrix}{A \times {\mathbb{e}}^{{j\mu}_{11}}} & {B \times {\mathbb{e}}^{{j\mu}_{12}}} \\{C \times {\mathbb{e}}^{{j\mu}_{21}}} & 0\end{pmatrix}} & {{Equation}\mspace{14mu} 423}\end{matrix}$

In Equation 423, A, B, and C are real numbers, μ₁₁, μ₁₂, and μ₂₁ arereal numbers, and the units of them are radians. In the scheme ofregularly hopping between precoding matrices over a period (cycle) withN slots, the precoding matrices prepared for the N slots are representedas follows.

Math 490

$\begin{matrix}{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{({\mathbb{i}})}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{({\mathbb{i}})}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{12}{({\mathbb{i}})}}})}}} & 0\end{pmatrix}} & {{Equation}\mspace{14mu} 424}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. Also, A, B, and C are fixedvalues regardless of i, and μ₁₁, μ₁₂, and μ₂₁ are fixed valuesregardless of i. If a matrix represented by the format of Equation 424is treated as a precoding matrix, “0” is present as one element of theprecoding matrix, thus it has an advantageous effect that the poorreception points described in other embodiments can be reduced.

Also, another basic precoding matrix different from that expressed byEquation 423 is expressed by the following equation.

Math 491

$\begin{matrix}{F = \begin{pmatrix}{A \times {\mathbb{e}}^{{j\mu}_{11}}} & {B \times {\mathbb{e}}^{{j\mu}_{12}}} \\0 & {D \times {\mathbb{e}}^{{j\mu}_{22}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 425}\end{matrix}$

In Equation 425, A, B, and C are real numbers, μ₁₁, μ₁₂, and μ₂₂ arereal numbers, and the units of them are radians. In the scheme ofregularly hopping between precoding matrices over a period (cycle) withN slots, the precoding matrices prepared for the N slots are representedas follows.

Math 492

$\begin{matrix}{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{({\mathbb{i}})}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{({\mathbb{i}})}}})}}} \\0 & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{({\mathbb{i}})}}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 426}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. Also, A, B, and D are fixedvalues regardless of i, and μ₁₁, μ₁₂, and μ₂₂ are fixed valuesregardless of i. If a matrix represented by the format of Equation 426is treated as a precoding matrix, “0” is present as one element of theprecoding matrix, thus it has an advantageous effect that the poorreception points described in other embodiments can be reduced.

Also, another basic precoding matrix different from those expressed byEquations 423 and 425 is expressed by the following equation.

Math 493

$\begin{matrix}{F = \begin{pmatrix}{A \times {\mathbb{e}}^{j\;\mu_{11}}} & 0 \\{C \times {\mathbb{e}}^{j\;\mu_{21}}} & {D \times {\mathbb{e}}^{j\;\mu_{22}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 427}\end{matrix}$

In Equation 427, A, C, and D are real numbers, μ₁₁, μ₂₁, and μ₂₂ arereal numbers, and the units of them are radians. In the scheme ofregularly hopping between precoding matrices over a period (cycle) withN slots, the precoding matrices prepared for the N slots are representedas follows.

Math 494

$\begin{matrix}{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 428}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. Also, A, C, and D are fixedvalues regardless of i, and μ₁₁, μ₂₁, and μ₂₂ are fixed valuesregardless of i. If a matrix represented by the format of Equation 428is treated as a precoding matrix, “0” is present as one element of theprecoding matrix, thus it has an advantageous effect that the poorreception points described in other embodiments can be reduced.

Also, another basic precoding matrix different from those expressed byEquations 423, 425, and 427 is expressed by the following equation.

Math 495

$\begin{matrix}{F = \begin{pmatrix}0 & {B \times {\mathbb{e}}^{j\;\mu_{12}}} \\{C \times {\mathbb{e}}^{j\;\mu_{21}}} & {D \times {\mathbb{e}}^{{j\mu}_{22}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 429}\end{matrix}$

In Equation 429, B, C, and D are real numbers, μ₁₂, μ₂₁, and μ₂₂ arereal numbers, and the units of them are radians. In the scheme ofregularly hopping between precoding matrices over a period (cycle) withN slots, the precoding matrices prepared for the N slots are representedas follows.

Math 496

$\begin{matrix}{{F\lbrack i\rbrack} = \begin{pmatrix}0 & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 430}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. Also, B, C, and D are fixedvalues regardless of i, and μ₁₂, μ₂₁, and μ₂₂ are fixed valuesregardless of i. If a matrix represented by the format of Equation 430is treated as a precoding matrix, “0” is present as one element of theprecoding matrix, thus it has an advantageous effect that the poorreception points described in other embodiments can be reduced. FromCondition #5 (Math 106) and Condition #6 (Math 107) in Embodiment 3, thefollowing conditions are important for achieving excellent datareception quality.

Math 497

Condition #69e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 498Condition #70e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

In order to distribute the poor reception points evenly with regards tophase in the complex plane, as described in Embodiment 6, Condition #71and Condition #72 are provided.

Math 499

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {{\mathbb{e}}^{j{(\frac{2\pi}{N})}}\mspace{14mu}{for}}}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{11mu},{N - 2}} \right)}}} & {{Condition}\mspace{14mu}{\# 71}}\end{matrix}$Math 500

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {{\mathbb{e}}^{j{({- \frac{2\pi}{N}})}}\mspace{14mu}{for}}}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}} & {{Condition}\mspace{14mu}{\# 72}}\end{matrix}$

With this structure, the reception device can avoid poor receptionpoints in the LOS environment, and thus can obtain the advantageouseffect of improving the data reception quality.

Note that, as an example of the above-described scheme for regularlyhopping between precoding matrices, there is a scheme for fixing θ₁₁(i)to 0 radians (θ₁₁(i) is set to a constant value regardless of i. In thiscase, θ₁₁(i) may be set to a value other than 0 radians.) so that θ₁₁(i)and θ₂₁(i) satisfy the above-described conditions. Also, there is ascheme for not fixing θ₁₁(i) to 0 radians, but fixing θ₂₁(i) to 0radians (θ₂₁(i) is set to a constant value regardless of i. In thiscase, θ₂₁(i) may be set to a value other than 0 radians.) so that θ₁₁(i)and θ₂₁(i) satisfy the above-described conditions.

The present embodiment describes the scheme of structuring N differentprecoding matrices for a precoding hopping scheme with an N-slot timeperiod (cycle). In this case, as the N different precoding matrices,F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared. In a singlecarrier transmission scheme, symbols are arranged in the order F[0],F[1], F[2], . . . , F[N−2], F[N−1] in the time domain (or the frequencydomain in the case of multi-carrier transmission scheme). However, thisis not the only example, and the N different precoding matrices F[0],F[1], F[2], . . . , F[N−2], F[N−1] generated according to the presentembodiment may be adapted to a multi-carrier transmission scheme such asan OFDM transmission scheme or the like. As in Embodiment 1, as a schemeof adaption in this case, precoding weights may be changed by arrangingsymbols in the frequency domain or in the frequency-time domains. Notethat a precoding hopping scheme with an N-slot time period (cycle) hasbeen described, but the same advantageous effects may be obtained byrandomly using N different precoding matrices. In other words, the Ndifferent precoding matrices do not necessarily need to be used in aregular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slotsN in the period (cycle) of the above scheme of regularly hopping betweenprecoding matrices), when the N different precoding matrices of thepresent embodiment are included, the probability of excellent receptionquality increases. In this case, Condition #69 and Condition #70 can bereplaced by the following conditions. (The number of slots in the period(cycle) is considered to be N.)

Math 501

Condition #73e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Math 502

Condition #74e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Embodiment 24

In Embodiment 10, the scheme for regularly hopping between precodingmatrices using a unitary matrix is described. However, the presentembodiment describes a scheme for regularly hopping between precodingmatrices using a matrix different from that used in Embodiment 10.

In the scheme of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

Math 503

$\begin{matrix}{{{Here},{i = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - 1.}}{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & 0\end{pmatrix}}} & {{Equation}\mspace{14mu} 431}\end{matrix}$

Here, let A, B, and C be real numbers, and μ₁₁, μ₁₂, and μ₂₁ be realnumbers expressed in radians. In addition, A, B, and C are fixed valuesnot depending on i. Similarly, μ₁₁, μ₁₂, and μ₂₁ are fixed values notdepending on i.

Math 504

$\begin{matrix}{{{{{For}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = \begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({v_{11} + {\psi_{11}{(i)}}})}}} & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{(i)}}})}}} \\0 & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{(i)}}})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 432}\end{matrix}$

Here, let α, β, and δ be real numbers, and ν₁₁, ν₁₂, and ν₂₂ be realnumbers expressed in radians. In addition, α, β, and δ are fixed valuesnot depending on i. Similarly, ν₁₁, ν₁₂, and ν₂₂ are fixed values notdepending on i.

The precoding matrices prepared for the 2N slots different from those inEquations 431 and 432 are represented by the following equations.

Math 505

$\begin{matrix}{{{{{For}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & 0\end{pmatrix}}} & {{Equation}\mspace{14mu} 433}\end{matrix}$

Here, let A, B, and C be real numbers, and μ₁₁, μ₁₂, and μ₂₁ be realnumbers expressed in radians. In addition, A, B, and C are fixed valuesnot depending on i. Similarly, μ₁₁, μ₁₂, and μ₂₁ are fixed values notdepending on i.

Math 506

$\begin{matrix}{{{{{For}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = \begin{pmatrix}0 & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{(i)}}})}}} \\{\gamma \times {\mathbb{e}}^{j{({v_{21} + {\psi_{21}{(i)}}})}}} & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{(i)}}})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 434}\end{matrix}$

Here, let β, γ, and δ be real numbers, and ν₁₂, ν₂₁, and ν₂₂ be realnumbers expressed in radians. In addition, β, γ, and δ are fixed valuesnot depending on i. Similarly, ν₁₂, ν₂₁, and ν₂₂ are fixed values notdepending on i.

The precoding matrices prepared for the 2N slots different from thosedescribed above are represented by the following equations.

Math 507

$\begin{matrix}{{{{{For}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}}})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 435}\end{matrix}$

Here, let A, C, and D be real numbers, and μ₁₁, μ₂₁, and μ₂₂ be realnumbers expressed in radians. In addition, A, C, and D are fixed valuesnot depending on i. Similarly, μ₁₁, μ₂₁, and μ₂₂ are fixed values notdepending on i.

Math 508

$\begin{matrix}{{{{{For}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = \begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({v_{11} + {\psi_{11}{(i)}}})}}} & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{(i)}}})}}} \\0 & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{(i)}}})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 436}\end{matrix}$

Here, let α, β, and δ be real numbers, and ν₁₁, ν₁₂, and ν₂₂ be realnumbers expressed in radians. In addition, α, β, and δ are fixed valuesnot depending on i. Similarly, ν₁₁, ν₁₂, and ν₂₂ are fixed values notdepending on i.

The precoding matrices prepared for the 2N slots different from thosedescribed above are represented by the following equations.

Math 509

$\begin{matrix}{{{{{For}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}}})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 437}\end{matrix}$

Here, let A, C, and D be real numbers, and μ₁₁, μ₂₁, and μ₂₂ be realnumbers expressed in radians. In addition, A, C, and D are fixed valuesnot depending on i. Similarly, μ₁₁, μ₂₁, and μ₂₂ are fixed values notdepending on i.

Math 510

$\begin{matrix}{{{{{For}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = \begin{pmatrix}0 & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{(i)}}})}}} \\{\gamma \times {\mathbb{e}}^{j{({v_{21} + {\psi_{21}{(i)}}})}}} & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{(i)}}})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 438}\end{matrix}$

Here, let β, γ, and δ be real numbers, and ν₁₂, ν₂₁, and ν₂₂ be realnumbers expressed in radians. In addition, β, γ, and δ are fixed valuesnot depending on i. Similarly, ν₁₂, ν₂₁, and ν₂₂ are fixed values notdepending on i.

Making the same considerations as in Condition #5 (Math 106) andCondition #6 (Math 107) of Embodiment 3, the following conditions areimportant for achieving excellent data reception quality.

Math 511

Condition #75e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Math 512

Condition #76e ^(j(ψ) ¹¹ ^((x)−ψ) ²¹ ^((x))) ≠e ^(j(ψ) ¹¹ ^((y)−ψ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)

(x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1,N+2, . . . , 2N−2,2N−1; and x≠y.)

Next, in order to distribute the poor reception points evenly withregards to phase in the complex plane, as described in Embodiment 6,Condition #77 or Condition #78 is provided.

Math 513

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {{\mathbb{e}}^{j{(\frac{2\pi}{N})}}\mspace{14mu}{for}}}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}} & {{Condition}\mspace{14mu}{\# 77}}\end{matrix}$Math 514

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\;\pi}{N}})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 78}}\end{matrix}$

Similarly, in order to distribute the poor reception points evenly withregards to phase in the complex plane, Condition #79 or Condition #80 isprovided.

Math 515

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\psi_{11}{({x + 1})}} - {\psi_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\psi_{11}{(x)}} - {\psi_{21}{(x)}}})}}} = {\mathbb{e}}^{j{(\frac{2\;\pi}{N})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 79}}\end{matrix}$Math 516

$\begin{matrix}{{\frac{{\mathbb{e}}^{j{({{\psi_{11}{({x + 1})}} - {\psi_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\psi_{11}{(x)}} - {\psi_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\;\pi}{N}})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 80}}\end{matrix}$

The above arrangement ensures to reduce the number of poor receptionpoints described in the other embodiments because one of the elements ofprecoding matrices is “0”. In addition, the reception device is enabledto improve reception quality because poor reception points areeffectively avoided especially in an LOS environment.

In an alternative scheme to the above-described precoding scheme ofregularly hopping between precoding matrices, θ₁₁(i) is fixed, forexample, to 0 radians (a fixed value not depending on i, and a valueother than 0 radians may be applicable) and θ₁₁(i) and θ₂₁(i) satisfythe conditions described above. In another alternative scheme, θ₂₁(i)instead of θ₁₁(i) is fixed, for example, to 0 radians (a fixed value notdepending on i, and a value other than 0 radians may be applicable) andθ₁₁(i) and θ₂₁(i) satisfy the conditions described above.

Similarly, in another alternative scheme, Ψ₁₁(i) is fixed, for example,to 0 radians (a fixed value not depending on i, and a value other than 0radians may be applicable) and Ψ₁₁(i) and Ψ₂₁(i) satisfy the conditionsdescribed above. Similarly, in another alternative scheme, Ψ₂₁(i)instead of Ψ₁₁(i) is fixed, for example, to 0 radians (a fixed value notdepending on i, and a value other than 0 radians may be applicable) andΨ₁₁(i) and Ψ₂₁(i) satisfy the conditions described above.

The present embodiment describes the scheme of structuring 2N differentprecoding matrices for a precoding hopping scheme with a 2N-slot timeperiod (cycle). In this case, as the 2N different precoding matrices,F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] are prepared. In a singlecarrier transmission scheme, symbols are arranged in the order F[0],F[1], F[2], . . . , F[2N−2], F[2N−1] in the time domain (or thefrequency domain in the case of multi-carrier). However, this is not theonly example, and the 2N different precoding matrices F[0], F[1], F[2],. . . , F[2N−2], F[2N−1] generated in the present embodiment may beadapted to a multi-carrier transmission scheme such as an OFDMtransmission scheme or the like. As in Embodiment 1, as a scheme ofadaption in this case, precoding weights may be changed by arrangingsymbols in the frequency domain or in the frequency-time domain. Notethat a precoding hopping scheme with a 2N-slot time period (cycle) hasbeen described, but the same advantageous effects may be obtained byrandomly using 2N different precoding matrices. In other words, the 2Ndifferent precoding matrices do not necessarily need to be used in aregular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slots2N in the period (cycle) of the above scheme of regularly hoppingbetween precoding matrices), when the 2N different precoding matrices ofthe present embodiment are included, the probability of excellentreception quality increases.

Embodiment 25

The present embodiment describes a scheme for increasing the period(cycle) size of precoding hops between the precoding matrices, byapplying Embodiment 17 to the precoding matrices described in Embodiment23.

As described in Embodiment 23, in the scheme of regularly hoppingbetween precoding matrices over a period (cycle) with N slots, theprecoding matrices prepared for the N slots are represented as follows.

Math 517

$\begin{matrix}{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & 0\end{pmatrix}} & {{Equation}\mspace{14mu} 439}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1. In addition, A, B, and C are fixedvalues not depending on i. Similarly, μ₁₁, μ₁₂, and μ₂₁ are fixed valuesnot depending on i. Furthermore, the N×M period (cycle) precodingmatrices based on Equation 439 are represented by the followingequation.

Math 518

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}} + X_{k}})}}} & 0\end{pmatrix}} & {{Equation}\mspace{14mu} 440}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.Precoding matrices F[0] to F[N×M−1] are thus generated (the precodingmatrices F[0] to F[N×M−1] may be in any order for the N×M slots in theperiod (cycle)). Symbol number N×M×i may be precoded using F[0], symbolnumber N×M×i+1 may be precoded using F[1], . . . , and symbol numberN×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . ,N×M−2, N×M−1). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality. Note that while the N×M period(cycle) precoding matrices have been set to Equation 440, the N×M period(cycle) precoding matrices may be set to the following equation, asdescribed above.

Math 519

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}} + X_{k}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}} + X_{k}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & 0\end{pmatrix}} & {{Equation}\mspace{14mu} 441}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.

As described in Embodiment 23, in the scheme of regularly hoppingbetween precoding matrices over a period (cycle) with N slots that isdifferent from the above-described N slots, the precoding matricesprepared for the N slots are represented as follows.

Math 520

$\begin{matrix}{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\0 & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 442}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1. In addition, A, B, and D are fixedvalues not depending on i. Similarly, μ₁₁, μ₁₂, and μ₂₂ are fixed valuesnot depending on i. Furthermore, the N×M period (cycle) precodingmatrices based on Equation 441 are represented by the followingequation.

Math 521

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\0 & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}} + X_{k}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 443}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.

Precoding matrices F[0] to F[N×M−1] are thus generated (the precodingmatrices F[0] to F[N×M−1] may be in any order for the N×M slots in theperiod (cycle)). Symbol number N×M×i may be precoded using F[0], symbolnumber N×M×i+1 may be precoded using F[1], . . . , and symbol numberN×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . ,N×M−2, N×M−1). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality. Note that while the N×M period(cycle) precoding matrices have been set to Equation 443, the N×M period(cycle) precoding matrices may be set to the following equation, asdescribed above.

Math 522

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}} + X_{k}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}} + X_{k}})}}} \\0 & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 444}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.

As described in Embodiment 23, in the scheme of regularly hoppingbetween precoding matrices over a period (cycle) with N slots that isdifferent from the above-described N slots, the precoding matricesprepared for the N slots are represented as follows.

Math 523

$\begin{matrix}{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 445}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1. In addition, A, C, and D are fixedvalues not depending on i. Similarly, μ₁₁, μ₂₁, and μ₂₂ are fixed valuesnot depending on i. Furthermore, the N×M period (cycle) precodingmatrices based on Equation 445 are represented by the followingequation.

Math 524

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}} + X_{k}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}} + X_{k}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 446}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.

Precoding matrices F[0] to F[N×M−1] are thus generated (the precodingmatrices F[0] to F[N×M−1] may be in any order for the N×M slots in theperiod (cycle)). Symbol number N×M×i may be precoded using F[0], symbolnumber N×M×i+1 may be precoded using F[1], . . . , and symbol numberN×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . ,N×M−2, N×M−1). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality. Note that while the N×M period(cycle) precoding matrices have been set to Equation 446, the N×M period(cycle) precoding matrices may be set to the following equation, asdescribed above.

Math 525

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}} + X_{k}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 447}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.

As described in Embodiment 23, in the scheme of regularly hoppingbetween precoding matrices over a period (cycle) with N slots that isdifferent from the above-described N slots, the precoding matricesprepared for the N slots are represented as follows.

Math 526

$\begin{matrix}{{F\lbrack i\rbrack} = \begin{pmatrix}0 & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 448}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1. In addition, B, C, and D are fixedvalues not depending on i. Similarly, μ₁₂, μ₂₁, and μ₂₂ are fixed valuesnot depending on i. Furthermore, the N×M period (cycle) precodingmatrices based on Equation 448 are represented by the followingequation.

Math 527

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = \begin{pmatrix}0 & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}} + X_{k}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}} + X_{k}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 449}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.

Precoding matrices F[0] to F[N×M−1] are thus generated (the precodingmatrices F[0] to F[N×M−1] may be in any order for the N×M slots in theperiod (cycle)). Symbol number N×M×i may be precoded using F[0], symbolnumber N×M×i+1 may be precoded using F[1], . . . , and symbol numberN×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . ,N×M−2, N×M−1). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality. Note that while the N×M period(cycle) precoding matrices have been set to Equation 449, the N×M period(cycle) precoding matrices may be set to the following equation, asdescribed above.

Math 528

$\begin{matrix}{{F\left\lbrack {{N \times k} + i} \right\rbrack} = \begin{pmatrix}0 & {B \times {\mathbb{e}}^{j{({\mu_{12} - {\theta_{11}{(i)}} + X_{k}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}}})}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 450}\end{matrix}$

Here, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.

The present embodiment describes the scheme of structuring N×M differentprecoding matrices for a precoding hopping scheme with N×M slots in thetime period (cycle). In this case, as the N×M different precodingmatrices, F[0], F[1], F[2], . . . , F[N×M−2], F[N×M−1] are prepared. Ina single carrier transmission scheme, symbols are arranged in the orderF[0], F[1], F[2], . . . , F[N×M−2], F[N×M−1] in the time domain (or thefrequency domain in the case of multi-carrier). However, this is not theonly example, and the N×M different precoding matrices F[0], F[1], F[2],. . . , F[N×M−2], F[N×M−1] generated in the present embodiment may beadapted to a multi-carrier transmission scheme such as an OFDMtransmission scheme or the like. As in Embodiment 1, as a scheme ofadaption in this case, precoding weights may be changed by arrangingsymbols in the frequency domain or in the frequency-time domain. Notethat a precoding hopping scheme with N×M slots in the time period(cycle) has been described, but the same advantageous effects may beobtained by randomly using N×M different precoding matrices. In otherwords, the N×M different precoding matrices do not necessarily need tobe used in a regular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slotsN×M in the period (cycle) of the above scheme of regularly hoppingbetween precoding matrices), when the N×M different precoding matricesof the present embodiment are included, the probability of excellentreception quality increases.

Embodiment 26

The present embodiment describes a scheme for increasing the period(cycle) size of precoding hops between the precoding matrices, byapplying Embodiment 20 to the precoding matrices described in Embodiment24.

In the scheme of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

Math 529

$\begin{matrix}{{{{For}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}} & {{Equation}\mspace{14mu} 451} \\{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & 0\end{pmatrix}} & \;\end{matrix}$

Here, let A, B, and C be real numbers, and μ₁₁, μ₁₂, and μ₂₁ be realnumbers expressed in radians. In addition, A, B, and C are fixed valuesnot depending on i. Similarly, μ₁₁, μ₁₂, and μ₂₁ are fixed values notdepending on i.

Math 530

$\begin{matrix}{{{{For}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}} & {{Equation}\mspace{14mu} 452} \\{{F\lbrack i\rbrack} = \begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({v_{11} + {\psi_{11}{(i)}}})}}} & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{(i)}}})}}} \\0 & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{(i)}}})}}}\end{pmatrix}} & \;\end{matrix}$

Here, let α, β, and δ be real numbers, and ν₁₁, ν₁₂, and ν₂₂ be realnumbers expressed in radians. In addition, α, β, and δ are fixed valuesnot depending on i. Similarly, ν₁₁, ν₁₂, and ν₂₂ are fixed values notdepending on i. Furthermore, the 2×N×M period (cycle) precoding matricesbased on Equations 451 and 452 are represented by the followingequation.

Math 531

$\begin{matrix}{\mspace{79mu}{{{{For}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}} & {{Equation}\mspace{14mu} 453} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}} + X_{k}})}}} & 0\end{pmatrix}} & \;\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

Math 532

$\begin{matrix}{\mspace{79mu}{{{{For}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}} & {{Equation}\mspace{14mu} 454} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({v_{11} + {\psi_{11}{(i)}}})}}} & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{(i)}}})}}} \\0 & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{(i)}} + Y_{k}})}}}\end{pmatrix}} & \;\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1. In addition, Xk=Yk may be true or Xk≠Ykmay be true.

Precoding matrices F[0] to F[2×N×M−1] are thus generated (the precodingmatrices F[0] to F[2×N×M−1] may be in any order for the 2×N×M slots inthe period (cycle)). Symbol number 2×N×M×i may be precoded using F[0],symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbolnumber 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . .. , 2×N×M−2, 2×N×M−1). (In this case, as described in previousembodiments, precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality.

The 2×N×M period (cycle) precoding matrices in Equation 453 may bechanged to the following equation.

Math 533

$\begin{matrix}{\mspace{79mu}{{{{For}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}} & {{Equation}\mspace{14mu} 455} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}} + X_{k}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}} + X_{k}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & 0\end{pmatrix}} & \;\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

The 2×N×M period (cycle) precoding matrices in Equation 454 may bechanged to the following equation.

Math 534

$\begin{matrix}{\mspace{79mu}{{{{For}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}} & {{Equation}\mspace{14mu} 456} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({v_{11} + {\psi_{11}{(i)}} + Y_{k}})}}} & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{(i)}} + Y_{k}})}}} \\0 & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{(i)}}})}}}\end{pmatrix}} & \;\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

Another example is shown below. In the scheme of regularly hoppingbetween precoding matrices over a period (cycle) with 2N slots, theprecoding matrices prepared for the 2N slots are represented as follows.

Math 535

$\begin{matrix}{{{{For}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}} & {{Equation}\mspace{14mu} 457} \\{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & 0\end{pmatrix}} & \;\end{matrix}$

Here, let A, B, and C be real numbers, and μ₁₁, μ₁₂, and μ₂₁ be realnumbers expressed in radians. In addition, A, B, and C are fixed valuesnot depending on i. Similarly, μ₁₁, μ₁₂, and μ₂₁ are fixed values notdepending on i.

Math 536

$\begin{matrix}{{{{For}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}} & {{Equation}\mspace{14mu} 458} \\{{F\lbrack i\rbrack} = \begin{pmatrix}0 & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{(i)}}})}}} \\{\gamma \times {\mathbb{e}}^{j{({v_{21} + {\psi_{21}{(i)}}})}}} & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{(i)}}})}}}\end{pmatrix}} & \;\end{matrix}$

Here, let β, γ, and δ be real numbers, and ν₁₂, ν₂₁, and ν₂₂ be realnumbers expressed in radians. In addition, β, γ, and δ are fixed valuesnot depending on i. Similarly, ν₁₂, ν₂₁, and ν₂₂ are fixed values notdepending on i. Furthermore, the 2×N×M period (cycle) precoding matricesbased on Equations 457 and 458 are represented by the followingequation.

Math 537

$\begin{matrix}{{{{For}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}} & {{Equation}\mspace{14mu} 459} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}} + X_{k}})}}} & 0\end{pmatrix}} & \;\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

Math 538

$\begin{matrix}{\mspace{79mu}{{{{For}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}} & {{Equation}\mspace{14mu} 460} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}0 & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{(i)}}})}}} \\{\gamma \times {\mathbb{e}}^{j{({v_{21} + {\psi_{21}{(i)}} + Y_{k}})}}} & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{(i)}} + Y_{k}})}}}\end{pmatrix}} & \;\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1. Furthermore, Xk=Yk may be true, or Xk≠Ykmay be true.

Precoding matrices F[0] to F[2×N×M−1] are thus generated (the precodingmatrices F[0] to F[2×N×M−1] may be in any order for the 2×N×M slots inthe period (cycle)). Symbol number 2×N×M×i may be precoded using F[0],symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbolnumber 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . .. , 2×N×M−2, 2×N×M−1). (In this case, as described in previousembodiments, precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality.

The 2×N×M period (cycle) precoding matrices in Equation 459 may bechanged to the following equation.

Math 539

$\begin{matrix}{\mspace{79mu}{{{{For}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}} & {{Equation}\mspace{14mu} 461} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}} + X_{k}})}}} & {B \times {\mathbb{e}}^{j{({\mu_{12} + {\theta_{11}{(i)}} + X_{k}})}}} \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & 0\end{pmatrix}} & \;\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

The 2×N×M period (cycle) precoding matrices in Equation 460 may bechanged to the following equation.

Math 540

$\begin{matrix}{\mspace{79mu}{{{{For}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}} & {{Equation}\mspace{14mu} 462} \\{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}0 & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{(i)}} + Y_{k}})}}} \\{\gamma \times {\mathbb{e}}^{j{({v_{21} + {\psi_{21}{(i)}}})}}} & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{(i)}}})}}}\end{pmatrix}} & \;\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

Another example is shown below. In the scheme of regularly hoppingbetween precoding matrices over a period (cycle) with 2N slots, theprecoding matrices prepared for the 2N slots are represented as follows.

Math 541

$\begin{matrix}{{{{For}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}} & {{Equation}\mspace{14mu} 463} \\{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{(i)}}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{(i)}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{(i)}}})}}}\end{pmatrix}} & \;\end{matrix}$

Here, let A, C, and D be real numbers, and μ₁₁, u₂₁, and μ₂₂ be realnumbers expressed in radians. In addition, A, C, and D are fixed valuesnot depending on i. Similarly, μ₁₁, μ₂₁, and μ₂₂ are fixed values notdepending on i.

Math 542

$\begin{matrix}{{For}{{i = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = \begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({v_{11} + {\psi_{11}{({\mathbb{i}})}}})}}} & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{({\mathbb{i}})}}})}}} \\0 & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{({\mathbb{i}})}}})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 464}\end{matrix}$

Here, let α, β, and δ be real numbers, and ν₁₁, ν₁₂, and ν₂₂ be realnumbers expressed in radians. In addition, α, β, and δ are fixed valuesnot depending on i. Similarly, ν₁₁, ν₁₂, and ν₂₂ are fixed values notdepending on i. Furthermore, the 2×N×M period (cycle) precoding matricesbased on Equations 463 and 464 are represented by the followingequation.

Math 543

$\begin{matrix}{\mspace{79mu}{{For}\mspace{79mu}{{i = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{({\mathbb{i}})}}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{({\mathbb{i}})}} + X_{k}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{({\mathbb{i}})}} + X_{k}})}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 465}\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

Math 544

$\begin{matrix}{\mspace{79mu}{{For}\mspace{79mu}{{i = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({v_{11} + {\psi_{11}{({\mathbb{i}})}}})}}} & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{({\mathbb{i}})}}})}}} \\0 & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{({\mathbb{i}})}} + Y_{k}})}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 466}\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1. Furthermore, Xk=Yk may be true, or Xk≠Ykmay be true.

Precoding matrices F[0] to F[2×N×M−1] are thus generated (the precodingmatrices F[0] to F[2×N×M−1] may be in any order for the 2×N×M slots inthe period (cycle)). Symbol number 2×N×M×i may be precoded using F[0],symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbolnumber 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . .. , 2×N×M−2, 2×N×M−1). (In this case, as described in previousembodiments, precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality.

The 2×N×M period (cycle) precoding matrices in Equation 465 may bechanged to the following equation.

Math 545

$\begin{matrix}{\mspace{79mu}{{For}\mspace{79mu}{{i = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{({\mathbb{i}})}} + X_{k}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{({\mathbb{i}})}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{({\mathbb{i}})}}})}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 467}\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

The 2×N×M period (cycle) precoding matrices in Equation 466 may bechanged to the following equation.

Math 546

$\begin{matrix}{\mspace{79mu}{{For}\mspace{79mu}{{i = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({v_{11} + {\psi_{11}{({\mathbb{i}})}} + Y_{k}})}}} & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{({\mathbb{i}})}} + Y_{k}})}}} \\0 & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{({\mathbb{i}})}}})}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 468}\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

Another example is shown below. In the scheme of regularly hoppingbetween precoding matrices over a period (cycle) with 2N slots, theprecoding matrices prepared for the 2N slots are represented as follows.

Math 547

$\begin{matrix}{{For}\text{}{{i = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{({\mathbb{i}})}}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{({\mathbb{i}})}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{({\mathbb{i}})}}})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 469}\end{matrix}$

Here, let A, C, and D be real numbers, and μ₁₁, μ₂₁, and μ₂₂ be realnumbers expressed in radians. In addition, A, C, and D are fixed valuesnot depending on i. Similarly, μ₁₁, μ₂₁, and μ₂₂ are fixed values notdepending on i.

Math 548

$\begin{matrix}{{For}\text{}{{i = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = \begin{pmatrix}0 & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{({\mathbb{i}})}}})}}} \\{\gamma \times {\mathbb{e}}^{j{({v_{21} + {\psi_{21}{({\mathbb{i}})}}})}}} & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{({\mathbb{i}})}}})}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 470}\end{matrix}$

Here, let β, γ, and δ be real numbers, and ν₁₂, ν₂₁, and ν₂₂ be realnumbers expressed in radians. In addition, β, γ, and δ are fixed valuesnot depending on i. Similarly, ν₁₂, ν₂₁, and ν₂₂ are fixed values notdepending on i. Furthermore, the 2×N×M period (cycle) precoding matricesbased on Equations 469 and 470 are represented by the followingequation.

Math 549

$\begin{matrix}{\mspace{79mu}{{For}\text{}\mspace{79mu}{{i = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{({\mathbb{i}})}}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{({\mathbb{i}})}} + X_{k}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{({\mathbb{i}})}} + X_{k}})}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 471}\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

Math 550

$\begin{matrix}{\mspace{79mu}{{For}\text{}\mspace{79mu}{{i = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}0 & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{({\mathbb{i}})}}})}}} \\{\gamma \times {\mathbb{e}}^{j{({v_{21} + {\psi_{21}{({\mathbb{i}})}} + Y_{k}})}}} & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{({\mathbb{i}})}} + Y_{k}})}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 472}\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1. Furthermore, Xk=Yk may be true, or Xk≠Ykmay be true.

Precoding matrices F[0] to F[2×N×M−1] are thus generated (the precodingmatrices F[0] to F[2×N×M−1] may be in any order for the 2×N×M slots inthe period (cycle)). Symbol number 2×N×M×i may be precoded using F[0],symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbolnumber 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . .. , 2×N×M−2, 2×N×M−1). (In this case, as described in previousembodiments, precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping scheme with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality.

The 2×N×M period (cycle) precoding matrices in Equation 471 may bechanged to the following equation.

Math 551

$\begin{matrix}{\mspace{79mu}{{For}\text{}\mspace{79mu}{{i = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}{A \times {\mathbb{e}}^{j{({\mu_{11} + {\theta_{11}{({\mathbb{i}})}} + X_{k}})}}} & 0 \\{C \times {\mathbb{e}}^{j{({\mu_{21} + {\theta_{21}{({\mathbb{i}})}}})}}} & {D \times {\mathbb{e}}^{j{({\mu_{22} + {\theta_{21}{({\mathbb{i}})}}})}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 473}\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

The 2×N×M period (cycle) precoding matrices in Equation 472 may bechanged to the following equation.

Math 552

$\begin{matrix}{\mspace{79mu}{{For}\text{}\mspace{79mu}{{i = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = \begin{pmatrix}0 & {\beta \times {\mathbb{e}}^{j{({v_{12} + {\psi_{11}{({\mathbb{i}})}} + Y_{k}})}}} \\{\gamma \times {\mathbb{e}}^{j{({v_{21} + {\psi_{21}{({\mathbb{i}})}}})}}} & {\delta \times {\mathbb{e}}^{j{({v_{22} + {\psi_{21}{({\mathbb{i}})}}})}}}\end{pmatrix}}}} & {{Equation}\mspace{14mu} 474}\end{matrix}$

Here, k=0, 1, . . . , M−2, M−1.

Focusing on poor reception points in the above examples, the followingconditions are important.

Math 553

Condition #81e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Math 554

Condition #82e ^(j(ψ) ¹¹ ^((x)−ψ) ²¹ ^((x))) ≠e ^(j(ψ) ¹¹ ^((y)−ψ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)

(x is N,N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . 2N−2,2N−1; and x≠y.)

Math 555

Condition #83θ₁₁(x)=θ₁₁(x+N) for ∀x(x=0,1,2, . . . ,N−2,N−1)andθ₂₁(y)=θ₂₁(y+N) for ∀y(y=0,1,2, . . . ,N−2,N−1)Math 556Condition #84ψ₁₁(x)=ψ₁₁(x+N) for ∀x(x=N,N+1,N+2, . . . ,2N−2,2N−1)andψ₂₁(y)=ψ₂₁(y+N) for ∀y(y=N,N+1,N+2, . . . ,2N−2,2N−1)

By satisfying the conditions shown above, excellent data receptionquality is achieved. Furthermore, the following conditions should besatisfied (See Embodiment 24).

Math 557

Condition #85e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Math 558

Condition #86e ^(j(ψ) ¹¹ ^((x)−ψ) ²¹ ^((x))) ≠e ^(j(ψ) ¹¹ ^((y)−ψ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)

(x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . 2N−2,2N−1; and x≠y.)

Focusing on Xk and Yk, the following conditions are noted.

Math 559

Condition #87X _(a) ≠X _(b)+2×s×π for ∀a,∀b(a≠b;a,b=0,1,2, . . . ,M−2,M−1)

(a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1; anda≠b.)

Here, s is an integer.

Math 560

Condition #88Y _(a) ≠Y _(b)+2×u×π for ∀a,∀b(a≠b;a,b=0,1,2, . . . ,M−2,M−1)

(a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1; anda≠b.)

(Here, u is an integer.)

By satisfying the two conditions shown above, excellent data receptionquality is achieved. In Embodiment 25, Condition #87 should besatisfied.

The present embodiment describes the scheme of structuring 2×N×Mdifferent precoding matrices for a precoding hopping scheme with 2N×Mslots in the time period (cycle). In this case, as the 2×N×M differentprecoding matrices, F[0], F[1], F[2], . . . , F[2×N×M−2], F[2×N×M−1] areprepared. In a single carrier transmission scheme, symbols are arrangedin the order F[0], F[1], F[2], . . . , F[2×N×M−2], F[2×N×M−1] in thetime domain (or the frequency domain in the case of multi-carrier).However, this is not the only example, and the 2×N×M different precodingmatrices F[0], F[1], F[2], . . . , F[2×N×M−2], F[2×N×M−1] generated inthe present embodiment may be adapted to a multi-carrier transmissionscheme such as an OFDM transmission scheme or the like.

As in Embodiment 1, as a scheme of adaption in this case, precodingweights may be changed by arranging symbols in the frequency domain orin the frequency-time domain. Note that a precoding hopping scheme with2×N×M slots the time period (cycle) has been described, but the sameadvantageous effects may be obtained by randomly using 2×N×M differentprecoding matrices. In other words, the 2×N×M different precodingmatrices do not necessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slots2×N×M in the period (cycle) of the above scheme of regularly hoppingbetween precoding matrices), when the 2×N×M different precoding matricesof the present embodiment are included, the probability of excellentreception quality increases.

Embodiment A1

In the present embodiment, a detailed description is given of a schemefor adapting the above-described transmission schemes that regularlyhops between precoding matrices to a communications system compliantwith the DVB (Digital Video Broadcasting)-T2 (T:Terrestrial) standard(DVB for a second generation digital terrestrial television broadcastingsystem).

FIG. 61 is an overview of the frame structure of a signal a signaltransmitted by a broadcast station according to the DVB-T2 standard.According to the DVB-T2 standard, an OFDM scheme is employed. Thus,frames are structured in the time and frequency domains. FIG. 61 showsthe frame structure in the time and frequency domains. The frame iscomposed of P1 Signalling data (6101), L1 Pre-Signalling data (6102), L1Post-Signalling data (6103), Common PLP (6104), and PLPs #1 to #N(6105_1 to 6105_N) (PLP: Physical Layer Pipe). (Here, L1 Pre-Signallingdata (6102) and L1 Post-Signalling data (6103) are referred to as P2symbols.) As above, the frame composed of P1 Signalling data (6101), L1Pre-Signalling data (6102), L1 Post-Signalling data (6103), Common PLP(6104), and PLPs #1 to #N (6105_1 to 6105_N) is referred to as a T2frame, which is a unit of frame structure.

The P1 Signalling data (6101) is a symbol for use by a reception devicefor signal detection and frequency synchronization (including frequencyoffset estimation). Also, the P1 Signalling data (6101) transmitsinformation including information indicating the FFT (Fast FourierTransform) size, and information indicating which of SISO (Single-InputSingle-Output) and MISO (Multiple-Input Single-Output) is employed totransmit a modulated signal. (The SISO scheme is for transmitting onemodulated signal, whereas the MISO scheme is for transmitting aplurality of modulated signals using space-time block coding.)

The L1 Pre-Signalling data (6102) transmits information including:information about the guard interval used in transmitted frames;information about PAPR (Peak to Average Power Ratio) method; informationabout the modulation scheme, error correction scheme (FEC: Forward ErrorCorrection), and coding rate of the error correction scheme all used intransmitting L1 Post-Signalling data; information about the size of L1Post-Signalling data and the information size; information about thepilot pattern; information about the cell (frequency region) uniquenumber; and information indicating which of the normal mode and extendedmode (the respective modes differs in the number of subcarriers used indata transmission) is used.

The L1 Post-Signalling data (6103) transmits information including:information about the number of PLPs; information about the frequencyregion used; information about the unique number of each PLP;information about the modulation scheme, error correction scheme, codingrate of the error correction scheme all used in transmitting the PLPs;and information about the number of blocks transmitted in each PLP.

The Common PLP (6104) and PLPs #1 to #N (6105_1 to 6105N) are fieldsused for transmitting data.

In the frame structure shown in FIG. 61, the P1 Signalling data (6101),L1 Pre-Signalling data (6102), L1 Post-Signalling data (6103), CommonPLP (6104), and PLPs #1 to #N (6105_1 to 6105_N) are illustrated asbeing transmitted by time-sharing. In practice, however, two or more ofthe signals are concurrently present. FIG. 62 shows such an example. Asshown in FIG. 62, L1 Pre-Signalling data, L1 Post-Signalling data, andCommon PLP may be present at the same time, and PLP#1 and PLP#2 may bepresent at the same time. That is, the signals constitute a frame usingboth time-sharing and frequency-sharing.

FIG. 63 shows an example of the structure of a transmission deviceobtained by applying the above-described schemes of regularly hoppingbetween precoding matrices to a transmission device compliant with theDVB-T2 standard (i.e., to a transmission device of a broadcast station).A PLP signal generating unit 6302 receives PLP transmission data(transmission data for a plurality of PLPs) 6301 and a control signal6309 as input, performs mapping of each PLP according to the errorcorrection scheme and modulation scheme indicated for the PLP by theinformation included in the control signal 6309, and outputs a(quadrature) baseband signal 6303 carrying a plurality of PLPs.

A P2 symbol signal generating unit 6305 receives P2 symbol transmissiondata 6304 and the control signal 6309 as input, performs mappingaccording to the error correction scheme and modulation scheme indicatedfor each P2 symbol by the information included in the control signal6309, and outputs a (quadrature) baseband signal 6306 carrying the P2symbols.

A control signal generating unit 6308 receives P1 symbol transmissiondata 6307 and P2 symbol transmission data 6304 as input, and thenoutputs, as the control signal 6309, information about the transmissionscheme (the error correction scheme, coding rate of the errorcorrection, modulation scheme, block length, frame structure, selectedtransmission schemes including a transmission scheme that regularly hopsbetween precoding matrices, pilot symbol insertion scheme, IFFT (InverseFast Fourier Transform)/FFT, method of reducing PAPR, and guard intervalinsertion scheme) of each symbol group shown in FIG. 61 (P1 Signallingdata (6101), L1 Pre-Signalling data (6102), L1 Post-Signalling data(6103), Common PLP (6104), PLPs #1 to #N (6105_1 to 6105_N)).

A frame structuring unit 6310 receives, as input, the baseband signal6303 carrying PLPs, the baseband signal 6306 carrying P2 symbols, andthe control signal 630. On receipt of the input, the frame structuringunit 6310 changes the order of input data in frequency domain and timedomain based on the information about frame structure included in thecontrol signal, and outputs a (quadrature) baseband signal 6311_1corresponding to stream 1 and a (quadrature) baseband signal 6311_2corresponding to stream 2 both in accordance with the frame structure.

A signal processing unit 6312 receives, as input, the baseband signal6311_1 corresponding to stream 1, the baseband signal 6311_2corresponding to stream 2, and the control signal 6309 and outputs amodulated signal 1 (6313_1) and a modulated signal 2 (6313_2) eachobtained as a result of signal processing based on the transmissionscheme indicated by information included in the control signal 6309. Thecharacteristic feature noted here lies in the following. That is, when atransmission scheme that regularly hops between precoding matrices isselected, the signal processing unit hops between precoding matrices andperforms weighting (precoding) in a manner similar to FIGS. 6, 22, 23,and 26. Thus, precoded signals so obtained are the modulated signal 1(6313_1) and modulated signal 2 (6313_2) obtained as a result of thesignal processing.

A pilot inserting unit 6314_1 receives, as input, the modulated signal 1(6313_1) obtained as a result of the signal processing and the controlsignal 6309, inserts pilot symbols into the received modulated signal 1(6313_1), and outputs a modulated signal 6315_1 obtained as a result ofthe pilot signal insertion. Note that the pilot symbol insertion iscarried out based on information indicating the pilot symbol insertionscheme included the control signal 6309.

A pilot inserting unit 6314_2 receives, as input, the modulated signal 2(6313_2) obtained as a result of the signal processing and the controlsignal 6309, inserts pilot symbols into the received modulated signal 2(6313_2), and outputs a modulated signal 6315_2 obtained as a result ofthe pilot symbol insertion. Note that the pilot symbol insertion iscarried out based on information indicating the pilot symbol insertionscheme included the control signal 6309.

An IFFT (Inverse Fast Fourier Transform) unit 6316_1 receives, as input,the modulated signal 6315_1 obtained as a result of the pilot symbolinsertion and the control signal 6309, and applies IFFT based on theinformation about the IFFT method included in the control signal 6309,and outputs a signal 6317_1 obtained as a result of the IFFT.

An IFFT unit 6316_2 receives, as input, the modulated signal 6315_2obtained as a result of the pilot symbol insertion and the controlsignal 6309, and applies IFFT based on the information about the IFFTmethod included in the control signal 6309, and outputs a signal 6317_2obtained as a result of the IFFT.

A PAPR reducing unit 6318_1 receives, as input, the signal 6317_1obtained as a result of the IFFT and the control signal 6309, performsprocessing to reduce PAPR on the received signal 6317_1, and outputs asignal 6319_1 obtained as a result of the PAPR reduction processing.Note that the PAPR reduction processing is performed based on theinformation about the PAPR reduction included in the control signal6309.

A PAPR reducing unit 6318_2 receives, as input, the signal 6317_2obtained as a result of the IFFT and the control signal 6309, performsprocessing to reduce PAPR on the received signal 6317_2, and outputs asignal 6319_2 obtained as a result of the PAPR reduction processing.Note that the PAPR reduction processing is carried out based on theinformation about the PAPR reduction included in the control signal6309.

A guard interval inserting unit 6320_1 receives, as input, the signal6319_1 obtained as a result of the PAPR reduction processing and thecontrol signal 6309, inserts guard intervals into the received signal6319_1, and outputs a signal 6321_1 obtained as a result of the guardinterval insertion. Note that the guard interval insertion is carriedout based on the information about the guard interval insertion schemeincluded in the control signal 6309.

A guard interval inserting unit 6320_2 receives, as input, the signal6319_2 obtained as a result of the PAPR reduction processing and thecontrol signal 6309, inserts guard intervals into the received signal6319_2, and outputs a signal 6321_2 obtained as a result of the guardinterval insertion. Note that the guard interval insertion is carriedout based on the information about the guard interval insertion schemeincluded in the control signal 6309.

A P1 symbol inserting unit 6322 receives, as input, the signal 6321_1obtained as a result of the guard interval insertion, the signal 6321_2obtained as a result of the guard interval insertion, and the P1 symboltransmission data 6307, generates a P1 symbol signal from the P1 symboltransmission data 6307, adds the P1 symbol to the signal 6321_1 obtainedas a result of the guard interval insertion, and adds the P1 symbol tothe signal 6321_2 obtained as a result of the guard interval insertion.Then, the P1 symbol inserting unit 6322 outputs a signal 6323_1 obtainedas a result of the processing related to P1 symbol and a signal 6323_2obtained as a result of the processing related to P1 symbol. Note that aP1 symbol signal may be added to both the signals 6323_1 and 6323_2 orto one of the signals 6323_1 and 6323_2. In the case where the P1 symbolsignal is added to one of the signals 6323_1 and 6323_2, the followingis noted. For purposes of description, an interval of the signal towhich a P1 symbol is added is referred to as a P1 symbol interval. Then,the signal to which a P1 signal is not added includes, as a basebandsignal, a zero signal in an interval corresponding to the P1 symbolinterval of the other signal. A wireless processing unit 6324_1 receivesthe signal 6323_1 obtained as a result of the processing related to P1symbol, performs processing such as frequency conversion, amplification,and the like, and outputs a transmission signal 6325_1. The transmissionsignal 6325_1 is then output as a radio wave from an antenna 6326_1.

A wireless processing unit 6324_2 receives the signal 6323_2 obtained asa result of the processing related to P1 symbol, performs processingsuch as frequency conversion, amplification, and the like, and outputs atransmission signal 6325_2. The transmission signal 6325_2 is thenoutput as a radio wave from an antenna 6326_2.

Next, a detailed description is given of the frame structure of atransmission signal and the transmission scheme of control information(information carried by the P1 symbol and P2 symbols) employed by abroadcast station (base station) in the case where the scheme ofregularly hopping between precoding matrices is adapted to a DVB-T2system.

FIG. 64 shows an example of the frame structure in the time andfrequency domains, in the case where a plurality of PLPs are transmittedafter transmission of P1 symbol, P2 symbols, and Common PLP. In FIG. 64,stream s1 uses subcarriers #1 to #M in the frequency domain. Similarly,stream s2 uses subcarriers #1 to #M in the frequency domain. Therefore,when streams s1 and s2 both have a symbol in the same subcarrier and atthe same time, symbols of the two streams are present at the samefrequency. In the case where precoding performed includes the precodingaccording to the scheme for regularly hopping between precoding matricesas described in the other embodiments, streams s1 and s2 are subjectedto weighting performed using the precoding matrices and z1 and z2 areoutput from the respective antennas.

As shown in FIG. 64, in interval 1, a symbol group 6401 of PLP #1 istransmitted using streams s1 and s2, and the data transmission iscarried out using the spatial multiplexing MIMO system shown in FIG. 49or the MIMO system with a fixed precoding matrix.

In interval 2, a symbol group 6402 of PLP #2 is transmitted using streams1, and the data transmission is carried out by transmitting onemodulated signal.

In interval 3, a symbol group 6403 of PLP #3 is transmitted usingstreams s1 and s2, and the data transmission is carried out using aprecoding scheme of regularly hopping between precoding matrices.

In interval 4, a symbol group 6404 of PLP #4 is transmitted usingstreams s1 and s2, and the data transmission is carried out usingspace-time block coding shown in FIG. 50. Note that the symbolarrangement used in space-time block coding is not limited to thearrangement in the time domain. Alternatively, the symbol arrangementmay be in the frequency domain or in symbol groups formed in the timeand frequency domains. In addition, the space-time block coding is notlimited to the one shown in FIG. 50.

In the case where a broadcast station transmits PLPs in the framestructure shown in FIG. 64, a reception device receiving thetransmission signal shown in FIG. 64 needs to know the transmissionscheme used for each PLP. As has been already described above, it istherefore necessary to transmit information indicating the transmissionscheme for each PLP, using L1 Post-Signalling data (6103 shown in FIG.61), which is a P2 symbol. The following describes an example of thescheme of structuring a P1 symbol used herein and the scheme ofstructuring a P2 symbol used herein.

Table 3 shows a specific example of control information transmittedusing a P1 symbol.

TABLE 3 S1 000: T2_SISO (One modulated signal transmission compliantwith DVB-T2 standard) 001: T2_MISO (Transmission using space-time blockcoding compliant with DVB-T2 standard) 010: NOT_T2 (compliant withstandard other than DVB-T2)

According to the DVB-T2 standard, the control information S1 (threebits) enables the reception device to determine whether or not theDVB-T2 standard is used and also to determine, if DVB-T2 is used, whichtransmission scheme is used. If the three bits are set to “000”, the S1information indicates that the modulated signal transmitted inaccordance with “transmission of a modulated signal compliant with theDVB-T2 standard”.

If the three bits are set to “001”, the S1 information indicates thatthe modulated signal transmitted is in accordance with “transmissionusing space-time block coding compliant with the DVB-T2 standard”.

In the DVB-T2 standard, the bit sets “010” to “111” are “Reserved” forfuture use. In order to adapt the present invention in a manner toestablish compatibility with the DVB-T2, the three bits constituting theS1 information may be set to “010” (or any bit set other than “000” and“001”) to indicate that the modulated signal transmitted is compliantwith a standard other than DVB-T2. On determining that the S1information received is set to “010”, the reception device is informedthat the modulated signal transmitted from the broadcast station iscompliant with a standard other than DVB-T2.

Next, a description is given of examples of the scheme of structuring aP2 symbol in the case where a modulated signal transmitted by thebroadcast station is compliant with a standard other than DVB-T2. Thefirst example is directed to a scheme in which P2 symbol compliant withthe DVB-T2 standard is used.

Table 4 shows a first example of control information transmitted usingL1 Post-Signalling data, which is one of P2 symbols.

TABLE 4 PLP_MODE 00: SISO/SIMO (2 bits) 01: MISO/MIMO (Space-time blockcode) 10: MIMO (Precoding scheme of regularly hopping between precodingmatrices) 11: MIMO (MIMO system with fixed precoding matrix or Spatialmultiplexing MIMO system)

SISO: Single-Input Single-Output (one modulated signal is transmittedand receive with one antenna)

SIMO: Single-Input Multiple-Output (one modulated signal is transmittedand received with a plurality of antennas)

MISO: Multiple-Input Single-Output (a plurality of modulated signals aretransmitted from a plurality of antennas and received with one antenna)

MIMO: Multiple-Input Multiple-Output (a plurality of modulated signalsare transmitted from a plurality of antennas and received with aplurality of antennas)

The 2-bit information “PLP_MODE” shown in Table 4 is control informationused to indicate the transmission scheme used for each PLP as shown inFIG. 64 (PLPs #1 to #4 in FIG. 64). That is, a separate piece of“PLP_MODE” information is provided for each PLP. That is, in the exampleshown in FIG. 64, PLP_MODE for PLP #1, PLP_MODE for PLP #2, PLP_MODE forPLP #3, PLP_MODE for PLP #4 . . . are transmitted from the broadcaststation. As a matter of course, by demodulating (and also performingerror correction) those pieces of information, the terminal at thereceiving end is enabled to recognize the transmission scheme that thebroadcast station used for transmitting each PLP.

When the PLP_MODE is set to “00”, the data transmission by acorresponding PLP is carried out by “transmitting one modulated signal”.When the PLP_MODE is set to “01”, the data transmission by acorresponding PLP is carried out by “transmitting a plurality ofmodulated signals obtained by space-time block coding”. When thePLP_MODE is set to “10”, the data transmission by a corresponding PLP iscarried out using a “precoding scheme of regularly hopping betweenprecoding matrices”. When the PLP_MODE is set to “11”, the datatransmission by a corresponding PLP is carried out using a “MIMO systemwith a fixed precoding matrix or spatial multiplexing MIMO system”.

Note that when the PLP_MODE is set to “01” to “11”, the informationindicating the specific processing conducted by the broadcast station(for example, the specific hopping scheme used in the scheme ofregularly hopping between precoding matrices, the specific space-timeblock coding scheme used, and the structure of precoding matrices used)needs to be notified to the terminal. The following describes the schemeof structuring control information that includes such information andthat is different from the example shown in Table 4.

Table 5 shows a second example of control information transmitted usingL1 Post-Signalling data, which is one of P2 symbols. The second exampleshown in Table 5 is different from the first example shown in Table 4.

TABLE 5 PLP_MODE (1 bit) 0: SISO/SIMO 1: MISO/MIMO (Space-time blockcoding, or Precoding scheme of regularly hopping between precodingmatrices, or MIMO system with fixed precoding matrix, or Spatialmultiplexing MIMO system) MIMO_MODE 0: Precoding scheme of regularlyhopping between (1 bit) precoding matrices --- OFF 1: Precoding schemeof regularly hopping between precoding matrices --- ON MIMO_PATTERN 00:Space-time block coding #1 (2 bits) 01: MIMO system with fixed precodingmatrix and Precoding matrix #1 10: MIMO system with fixed precodingmatrix and Precoding matrix #2 11: Spatial multiplexing MIMO systemMIMO_PATTERN 00: Precoding scheme of regularly hopping between #2 (2bits) precoding matrices, using precoding matrix hopping scheme #1 01:Precoding scheme of regularly hopping between precoding matrices, usingprecoding matrix hopping scheme #2 10: Precoding scheme of regularlyhopping between recoding matrices, using precoding matrix hopping scheme#3 11: Precoding scheme of regularly hopping between precoding matrices,using precoding matrix hopping scheme #4

As shown in Table 5, the control information includes “PLP_MODE” whichis one bit long, “MIMO_MODE” which is one bit long, “MIMO_PATTERN #1”which is two bits long, and “MIMO_PATTERN #2” which is two bits long. Asshown in FIG. 64, these four pieces of control information is to notifythe transmission scheme of a corresponding one of PLPs (PLPs #1 to #4 inthe example shown in FIG. 64). Thus, a set of four pieces of informationis provided for each PLP. That is, in the example shown in FIG. 64, thebroadcast station transmits a set of PLP_MODE information, MIMO_MODEinformation, MIMO_PATTERN #1 information, and MIMO_PATTERN #2information for PLP #1, a set of PLP_MODE information, MIMO_MODEinformation, MIMO_PATTERN #1 information, and MIMO_PATTERN #2information for PLP #2, a set of PLP_MODE information, MIMO_MODEinformation, MIMO_PATTERN #1 information, and MIMO_PATTERN #2information for PLP #3, a set of PLP_MODE information, MIMO_MODEinformation, MIMO_PATTERN #1 information, and MIMO_PATTERN #2information for PLP #4 . . . . As a matter of course, by demodulating(and also performing error correction) those pieces of information, theterminal at the receiving end is enabled to recognize the transmissionscheme that the broadcast station used for transmitting each PLP.

With the PLP_MODE set to “0”, the data transmission by a correspondingPLP is carried out by “transmitting one modulated signal”. With thePLP_MODE set to “1”, the data transmission by a corresponding PLP iscarried out by “transmitting a plurality of modulated signals obtainedby space-time block coding”, “precoding scheme of regularly hoppingbetween precoding matrices”, “MIMO system with a fixed precodingmatrix”, or “spatial multiplexing MIMO system”.

With the “PLP_MODE” set to “1”, the “MIMO_MODE” information is madeeffective. With “MIMO_MODE” set to “0”, data transmission is carried outby a scheme other than the “precoding scheme of regularly hoppingbetween precoding matrices”. With “MIMO_MODE” set to “1”, on the otherhand, data transmission is carried out by the “precoding scheme ofregularly hopping between precoding matrices”.

With “PLP_MODE” set to “1” and “MIMO_MODE” set to “0”, the “MIMO_PATTERN#1” information is made effective. With “MIMO_PATTERN #1” set to “00”,data transmission is carried out using space-time block coding. With“MIMO_PATTERN” set to “01”, data transmission is carried out using aprecoding scheme in which weighting is performed using a fixed precodingmatrix #1. With “MIMO_PATTERN” set to “10”, data transmission is carriedout using a precoding scheme in which weighting is performed using afixed precoding matrix #2 (Note that the precoding matrix #1 andprecoding matrix #2 are mutually different). When “MIMO_PATTERN” set to“11”, data transmission is carried out using spatial multiplexing MIMOsystem (Naturally, it may be construed that Scheme 1 shown in FIG. 49 isselected here).

With “PLP_MODE” set to “1” and “MIMO_MODE” set to “1”, the “MIMO_PATTERN#2” information is made effective. Then, with “MIMO_PATTERN #2” set to“00”, data transmission is carried out using the precoding matrixhopping scheme #1 according to which precoding matrices are regularlyhopped. With “MIMO_PATTERN #2” set to “01”, data transmission is carriedout using the precoding matrix hopping scheme #2 according to whichprecoding matrices are regularly hopped. With “MIMO_PATTERN #2” set to“10”, data transmission is carried out using the precoding matrixhopping scheme #3 according to which precoding matrices are regularlyhopped. With “MIMO_PATTERN #2” set to “11”, data transmission is carriedout using the precoding matrix hopping scheme #4 according to whichprecoding matrices are regularly hopped. Note that the precoding matrixhopping schemes #1 to #4 are mutually different. Here, to define ascheme being different, it is supposed that #A and #B are mutuallydifferent schemes and then one of the following is true.

-   -   The precoding matrices used in #A include the same matrices used        in #B but the periods (cycles) of the matrices are different.    -   The precoding matrices used in #A include precoding matrices not        used in #B.    -   None of the precoding matrices used in #A is used in #B.

In the above description, the control information shown in Tables 4 and5 is transmitted on L1 Post-Signalling data, which is one of P2 symbols.According to the DVB-T2 standard, however, the amount of informationthat can be transmitted as P2 symbols is limited. Therefore, addition ofinformation shown in Tables 4 and 5 to the information required in theDVB-T2 standard to be transmitted using P2 symbols may result in anamount exceeding the maximum amount that can be transmitted as P2symbols. In such a case, Signalling PLP (6501) may be provided as shownin FIG. 65 to transmit control information required by a standard otherthan the DVB-T2 standard (that is, data transmission is carried outusing both L1 Post-Signalling data and Signalling PLP). In the exampleshown in FIG. 65, the same frame structure as shown in FIG. 61 is used.However, the frame structure is not limited to this specific example.For example, similarly to L1 Pre-signalling data and other data shown inFIG. 62, Signalling PLP may be allocated to a specific carrier range ina specific time domain in the time and frequency domains. In short,Signalling PLP may be allocated in the time and frequency domains in anyway.

As described above, the present embodiment allows for choice of a schemeof regularly hopping between precoding matrices while using amulti-carrier scheme, such as an OFDM scheme, without compromising thecompatibility with the DVB-T2 standard. This offers the advantages ofobtaining high reception quality, as well as high transmission speed, inan LOS environment. While in the present embodiment, the transmissionschemes to which a carrier group can be set are “a spatial multiplexingMIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO schemefor regularly hopping between precoding matrices, space-time blockcoding, or a transmission scheme for transmitting only stream s1”, butthe transmission schemes are not limited in this way. Furthermore, theMIMO scheme using a fixed precoding matrix limited to scheme #2 in FIG.49, as any structure with a fixed precoding matrix is acceptable.

Furthermore, the above description is directed to a scheme in which theschemes selectable by the broadcast station are “a spatial multiplexingMIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO schemefor regularly hopping between precoding matrices, space-time blockcoding, or a transmission scheme for transmitting only stream s1”.However, it is not necessary that all of the transmission schemes areselectable. Any of the following examples is also possible.

-   -   A transmission scheme in which any of the following is        selectable: a MIMO scheme using a fixed precoding matrix, a MIMO        scheme for regularly hopping between precoding matrices,        space-time block coding, and a transmission scheme for        transmitting only stream s1.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme using a fixed precoding matrix, a MIMO        scheme for regularly hopping between precoding matrices, and        space-time block coding.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme using a fixed precoding matrix, a MIMO        scheme for regularly hopping between precoding matrices, and a        transmission scheme for transmitting only stream s1.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme for regularly hopping between        precoding matrices, space-time block coding, and a transmission        scheme for transmitting only stream s1.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme using a fixed precoding matrix, and a        MIMO scheme for regularly hopping between precoding matrices.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme for regularly hopping between        precoding matrices, and space-time block coding.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme for regularly hopping between        precoding matrices, and a transmission scheme for transmitting        only stream s1.        As listed above, as long as a MIMO scheme for regularly hopping        between precoding matrices is included as a selectable scheme,        the advantageous effects of high-speed data transmission is        obtained in an LOS environment, in addition to excellent        reception quality for the reception device.

Here, it is necessary to set the control information S1 in P1 symbols asdescribed above. In addition, as P2 symbols, the control information maybe set differently from a scheme (the scheme for setting thetransmission scheme of each PLP) shown in Table 4. Table 6 shows oneexample of such a scheme.

TABLE 6 PLP-MODE 00: SISO/SIMO (2 bits) 01: MISO/MIMO (Space-time blockcode) 10: MIMO (Precoding scheme of regularly hopping between precodingmatrices) 11: Reserved

Table 6 differs from Table 4 in that the “PLP_MODE” set to “11” is“Reserved.” In this way, the number of bits constituting the “PLP_MODE”shown in Tables 4 and 6 may be increased or decreased depending on thenumber of selectable PLP transmission schemes, in the case where theselectable transmission schemes are as shown in the above examples.

The same holds with respect to Table 5. For example, if the only MIMOscheme supported is a precoding scheme of regularly hopping betweenprecoding matrices, the control information “MIMO_MODE” is no longernecessary. Furthermore, the control information “MIMO_PATTERN #1” maynot be necessary in the case, for example, where a MIMO scheme using afixed precoding matrix is not supported. Furthermore, the controlinformation “MIMO_PATTERN #1” may be one bit long instead of two bitslong, in the case where, for example, no more than one precoding matrixis required for a MIMO scheme using a fixed precoding matrix.Furthermore, the control information “MIMO_PATTERN #1” may be two bitslong or more in the case where a plurality of precoding matrices areselectable.

The same applies to “MIMO_PATTERN #2”. That is, the control information“MIMO_PATTERN #2” may be one bit long instead of two bits long, in thecase where no more than one precoding scheme of regularly hoppingbetween precoding matrices is available. Alternatively, the controlinformation “MIMO_PATTERN #2” may be two bits long or more in the casewhere a plurality of precoding schemes of regularly hopping betweenprecoding matrices are selectable.

In the present embodiment, the description is directed to thetransmission device having two antennas, but the number of antennas isnot limited to two. With a transmission device having more than twoantennas, the control information may be transmitted in the same manner.Yet, to enable the modulated signal transmission with the use of fourantennas in addition to the modulated signal transmission with the useof two antennas, there may be a case where the number of bitsconstituting respective pieces of control information needs to beincreased. In such a modification, it still holds that the controlinformation is transmitted by the P1 symbol and the control informationis transmitted by P2 symbols as set forth above.

The above description is directed to the frame structure of PLP symbolgroups transmitted by a broadcast station in a time-sharing transmissionscheme as shown in FIG. 64.

FIG. 66 shows another example of a symbol arranging scheme in the timeand frequency domains, which is different from the symbol arrangingscheme shown in FIG. 64. The symbols shown in FIG. 66 are of the streams1 and s2 and to be transmitted after the transmission of P1 symbol, P2symbols, and Common PLP. In FIG. 66, each symbol denoted by “#1”represents one symbol of the symbol group of PLP #1 shown in FIG. 64.Similarly, each symbol denoted as “#2” represents one symbol of thesymbol group of PLP #2 shown in FIG. 64, each symbol denoted as “#3”represents one symbol of the symbol group of PLP #3 shown in FIG. 64,and each symbol denoted as “#4” represents one symbol of the symbolgroup of PLP #4 shown in FIG. 64. Similarly to FIG. 64, PLP #1 transmitsdata using spatial multiplexing MIMO system shown in FIG. 49 or the MIMOsystem with a fixed precoding matrix. In addition, PLP #2 transmits datathereby to transmit one modulated signal. PLP #3 transmits data using aprecoding scheme of regularly hopping between precoding matrices. PLP #4transmits data using space-time block coding shown in FIG. 50. Note thatthe symbol arrangement used in space-time block coding is not limited tothe arrangement in the time domain. Alternatively, the symbolarrangement may be in the frequency domain or in symbol groups formed inthe time and frequency domains. In addition, space-time block coding isnot limited to the one shown in FIG. 50.

In FIG. 66, where streams s1 and s2 both have a symbol in the samesubcarrier and at the same time, symbols of the two streams are presentat the same frequency. In the case where precoding performed includesthe precoding according to the scheme for regularly hopping betweenprecoding matrices as described in the other embodiments, streams s1 ands2 are subjected to weighting performed using the precoding matrices,and z1 and z2 are output from the respective antennas.

FIG. 66 differs from FIG. 64 in the following points. That is, theexample shown in FIG. 64 is an arrangement of a plurality of PLPs usingtime-sharing, whereas the example shown in FIG. 66 is an arrangement ofa plurality of PLPs using both time-sharing and frequency-sharing. Thatis, for example, at time 1, a symbol of PLP #1 and a symbol of PLP #2are both present. Similarly, at time 3, a symbol of PLP #3 and a symbolof PLP #4 are both present. In this way, PLP symbols having differentindex numbers (#X; X=1, 2 . . . ) may be allocated on a symbol-by-symbolbasis (for each symbol composed of one subcarrier per time).

For the sake of simplicity, FIG. 66 only shows symbols denoted by “#1”and “#2” at time 1. However, this is not a limiting example, and PLPsymbols having any index numbers other than “#1” and “#2” may be presentat time 1. In addition, the relation between subcarriers present at time1 and PLP index numbers are not limited to that shown in FIG. 66.Alternatively, a PLP symbol having any index number may be allocated toany subcarrier. Similarly, in addition, a PLP symbol having any indexnumber may be allocated to any subcarrier at any time other than time 1.

FIG. 67 shows another example of a symbol arranging scheme in the timeand frequency domains, which is different from the symbol arrangingscheme shown in FIG. 64. The symbols shown in FIG. 67 are of the streams1 and s2 and to be transmitted after the transmission of P1 symbol, P2symbols, and Common PLP. The characterizing feature of the example shownin FIG. 67 is that the “transmission scheme for transmitting only streams1” is not selectable in the case where PLP transmission for T2 framesis carried out basically with a plurality of antennas.

Therefore, data transmission by the symbol group 6701 of PLP #1 shown inFIG. 67 is carried out by “a spatial multiplexing MIMO system or a MIMOscheme using a fixed precoding matrix”. Data transmission by the symbolgroup 6702 of PLP #2 is carried out using “a precoding scheme ofregularly hopping between precoding matrices”. Data transmission by thesymbol group 6703 of PLP #3 is carried out by “space-time block coding”.Note that data transmission by the PLP symbol group 6703 of PLP #3 andthe following symbol groups in T2 frame is carried out by using one of“a spatial multiplexing MIMO system or a MIMO scheme using a fixedprecoding matrix,” “a precoding scheme of regularly hopping betweenprecoding matrices” and “space-time block coding”.

FIG. 68 shows another example of a symbol arranging scheme in the timeand frequency domains, which is different from the symbol arrangingscheme shown in FIG. 66. The symbols shown in FIG. 66 are of the streams1 and s2 and to be transmitted after the transmission of P1 symbol, P2symbols, and Common PLP. In FIG. 68, each symbol denoted by “#1”represents one symbol of the symbol group of PLP #1 shown in FIG. 67.Similarly, each symbol denoted as “#2” represents one symbol of thesymbol group of PLP #2 shown in FIG. 67, each symbol denoted as “#3”represents one symbol of the symbol group of PLP #3 shown in FIG. 67,and each symbol denoted as “#4” represents one symbol of the symbolgroup of PLP #4 shown in FIG. 67. Similarly to FIG. 67, PLP #1 transmitsdata using spatial multiplexing MIMO system shown in FIG. 49 or the MIMOsystem with a fixed precoding matrix. PLP #2 transmits data using aprecoding scheme of regularly hopping between precoding matrices. PLP #3transmits data using space-time block coding shown in FIG. 50. Note thatthe symbol arrangement used in the space-time block coding is notlimited to the arrangement in the time domain. Alternatively, the symbolarrangement may be in the frequency domain or in symbol groups formed inthe time and frequency domains. In addition, the space-time block codingis not limited to the one shown in FIG. 50.

In FIG. 68, where streams s1 and s2 both have a symbol in the samesubcarrier and at the same time, symbols of the two streams are presentat the same frequency. In the case where precoding performed includesthe precoding according to the scheme for regularly hopping betweenprecoding matrices as described in the other embodiments, streams s1 ands2 are subjected to weighting performed using the precoding matrices andz1 and z2 are output from the respective antennas.

FIG. 68 differs from FIG. 67 in the following points. That is, theexample shown in FIG. 67 is an arrangement of a plurality of PLPs usingtime-sharing, whereas the example shown in FIG. 68 is an arrangement ofa plurality of PLPs using both time-sharing and frequency-sharing. Thatis, for example, at time 1, a symbol of PLP #1 and a symbol of PLP #2are both present. In this way, PLP symbols having different indexnumbers (#X; X=1, 2 . . . ) may be allocated on a symbol-by-symbol basis(for each symbol composed of one subcarrier per time).

For the sake of simplicity, FIG. 68 only shows symbols denoted by “#1”and “#2” at time 1. However, this is not a limiting example, and PLPsymbols having any index numbers other than “#1” and “#2” may be presentat time 1. In addition, the relation between subcarriers present at time1 and PLP index numbers are not limited to that shown in FIG. 68.Alternatively, a PLP symbol having any index number may be allocated toany subcarrier. Similarly, in addition, a PLP symbol having any indexnumber may be allocated to any subcarrier at any time other than time 1.Alternatively, on the other hand, only one PLP symbol may be allocatedat a specific time as at time t3. That is, in a framing scheme ofarranging PLP symbols in the time and frequency domains, any allocationis applicable.

As set forth above, no PLPs using “a transmission scheme fortransmitting only stream s1” exist in the T2 frame, so that the dynamicrange of a signal received by the terminal is ensured to be narrow. As aresult, the advantageous effect is achieved that the probability ofexcellent reception quality increases.

Note that the description of FIG. 68 is described using an example inwhich the transmission scheme selected is one of “spatial multiplexingMIMO system or a MIMO scheme using a fixed precoding matrix”, “aprecoding scheme of regularly hopping between precoding matrices”, and“space-time block coding”. Yet, it is not necessary that all of thesetransmission schemes are selectable. For example, the followingcombinations of the transmission schemes may be made selectable.

-   -   “a precoding scheme of regularly hopping between precoding        matrices”, “space-time block coding”, and “a MIMO scheme using a        fixed precoding matrix” are selectable.    -   “a precoding scheme of regularly hopping between precoding        matrices” and “space-time block coding” are selectable.    -   “a precoding scheme of regularly hopping between precoding        matrices” and “a MIMO scheme using a fixed precoding matrix” are        selectable.

The above description relates to an example in which the T2 frameincludes a plurality of PLPs. The following describes an example inwhich T2 frame includes one PLP only.

FIG. 69 shows an example of frame structure in the time and frequencydomains for stream s1 and s2 in the case where only one PLP exits in T2frame. In FIG. 69, the denotation “control symbol” represents a symbolsuch as P1 symbol, P2 symbol, or the like. In the example shown in FIG.69, the first T2 frame is transmitted using interval 1. Similarly, thesecond T2 frame is transmitted using interval 2, the third T2 frame istransmitted using interval 3, and the fourth T2 frame is transmittedusing interval 4.

In the example shown in FIG. 69, in the first T2 frame, a symbol group6801 for PLP #1-1 is transmitted and the transmission scheme selected is“spatial multiplexing MIMO system or MIMO scheme using a fixed precodingmatrix”.

In the second T2 frame, a symbol group 6802 for PLP #2-1 is transmittedand the transmission scheme selected is “a scheme for transmitting onemodulated signal”.

In the third T2 frame, a symbol group 6803 for PLP #3-1 is transmittedand the transmission scheme selected is “a precoding scheme of regularlyhopping between precoding matrices”.

In the fourth T2 frame, a symbol group 6804 for PLP #4-1 is transmittedand the transmission scheme selected is “space-time block coding”. Notethat the symbol arrangement used in the space-time block coding is notlimited to the arrangement in the time domain. Alternatively, the symbolarrangement may be in the frequency domain or in symbol groups formed inthe time and frequency domains. In addition, the space-time block codingis not limited to the one shown in FIG. 50.

In FIG. 69, where streams s1 and s2 both have a symbol in the samesubcarrier and at the same time, symbols of the two streams are presentat the same frequency. In the case where precoding performed includesthe precoding according to the scheme for regularly hopping betweenprecoding matrices as described in the other embodiments, streams s1 ands2 are subjected to weighting performed using the precoding matrices andz1 and z2 are output from the respective antennas.

In the above manner, a transmission scheme may be set for each PLP inconsideration of the data transmission speed and the data receptionquality at the receiving terminal, so that increase in data transmissionseeped and excellent reception quality are both achieved. As an examplescheme of structuring control information, the control informationindicating, for example, the transmission scheme and other informationof P1 symbol and P2 symbols (and also Signalling PLP where applicable)may be configured in a similar manner to Tables 3-6. The difference isas follows. In the frame structure shown, for example, in FIG. 64, oneT2 frame includes a plurality of PLPs. Thus, it is necessary to providethe control information indicating the transmission scheme and the likefor each PLP. On the other hand, in the frame structure shown, forexample, in FIG. 69, one T2 frame includes one PLP only. Thus, it issufficient to provide the control information indicating thetransmission scheme and the like only for the one PLP.

Although the above description is directed to the scheme of transmittinginformation about the PLP transmission scheme using P1 symbol and P2symbols (and Signalling PLPs where applicable), the following describesin particular the scheme of transmitting information about the PLPtransmission scheme without using P2 symbols.

FIG. 70 shows a frame structure in the time and frequency domains forthe case where a terminal at a receiving end of data broadcasting by abroadcast station supporting a standard other than the DVB-T2 standard.In FIG. 70, the same reference signs are used to denote the blocks thatoperate in a similar way to those shown in FIG. 61. The frame shown inFIG. 70 is composed of P1 Signalling data (6101), first Signalling data(7001), second Signalling data (7002), Common PLP (6104), and PLPs #1 toN (6105_1 to 6105_N) (PLP: Physical Layer Pipe). In this way, a framecomposed of P1 Signalling data (6101), first Signalling data (7001),second Signalling data (7002), Common PLP (6104), PLPs #1 to N (6105_1to 6105_N) constitutes one frame unit.

By the P1 Signalling data (6101), data indicating that the symbol is fora reception device to perform signal detection and frequencysynchronization (including frequency offset estimation) is transmitted.In this example, in addition, data identifying whether or not the framesupports the DVB-T2 standard needs to be transmitted. For example, by S1shown in Table 3, data indicating whether or not the signal supports theDVB-T2 standard needs to be transmitted.

By the first 1 Signalling data (7001), the following information may betransmitted for example: information about the guard interval used inthe transmission frame; information about the method of PAPR (Peak toAverage Power Ratio); information about the modulation scheme, errorcorrection scheme, coding rate of the error correction scheme all ofwhich are used in transmitting the second Signalling data; informationabout the size of the second Signalling data and about information size;information about the pilot pattern; information about the cell(frequency domain) unique number; and information indicating which ofthe norm mode and extended mode is used. Here, it is not necessary thatthe first Signalling data (7001) transmits data supporting the DVB-T2standard. By L2 Post-Signalling data (7002), the following informationmay be transmitted for example: information about the number of PLPs;information about the frequency domain used; information about theunique number of each PLP; information about the modulation scheme,error correction scheme, coding rate of the error correction scheme allof which are used in transmitting the PLPs; and information about thenumber of blocks transmitted in each PLP.

In the frame structure shown in FIG. 70, first Signalling data (7001),second Signalling data (7002), L1 Post-Signalling data (6103), CommonPLP (6104), PLPs #1 to #N (6105_1 to 6105_N) are appear to betransmitted by time sharing. In practice, however, two or more of thesignals are concurrently present. FIG. 71 shows such an example. Asshown in FIG. 71, first Signalling data, second Signalling data, andCommon PLP may be present at the same time, and PLP #1 and PLP #2 may bepresent at the same time. That is, the signals constitute a frame usingboth time-sharing and frequency-sharing.

FIG. 72 shows an example of the structure of a transmission deviceobtained by applying the above-described schemes of regularly hoppingbetween precoding matrices to a transmission device (of a broadcaststation, for example) that is compliant with a standard other than theDVB-T2 standard. In FIG. 72, the same reference signs are used to denotethe components that operate in a similar way to those shown in FIG. 63and the description of such components are the same as above. A controlsignal generating unit 6308 receives transmission data 7201 for thefirst and second Signalling data, transmission data 6307 for P1 symbolas input. As output, the control signal generating unit 6308 outputs acontrol signal 6309 carrying information about the transmission schemeof each symbol group shown in FIG. 70. (The information about thetransmission scheme output herein includes: error correction coding,coding rate of the error correction, modulation scheme, block length,frame structure, the selected transmission schemes including atransmission scheme that regularly hops between precoding matrices,pilot symbol insertion scheme, information about IFFT (Inverse FastFourier Transform)/FFT and the like, information about the method ofreducing PAPR, and information about guard interval insertion scheme.)

The control signal generating unit 7202 receives the control signal 6309and the transmission data 7201 for first and second Signalling data asinput. The control signal generating unit 7202 then performs errorcorrection coding and mapping based on the modulation scheme, accordingto the information carried in the control signal 6309 (namely,information about the error correction of the first and secondSignalling data, information about the modulation scheme) and outputs a(quadrature) baseband signal 7203 of the first and second Signallingdata.

Next, a detailed description is given of the frame structure of atransmission signal and the transmission scheme of control information(information carried by the P1 symbol and first and second 2 Signallingdata) employed by a broadcast station (base station) in the case wherethe scheme of regularly hopping between precoding matrices is adapted toa system compliant with a standard other than the DVB-T2 standard.

FIG. 64 shows an example of the frame structure in the time andfrequency domains, in the case where a plurality of PLPs are transmittedafter transmission of P1 symbol, first and second 2 Signalling data, andCommon PLP. In FIG. 64, stream s1 uses subcarriers #1 to #M in thefrequency domain. Similarly, stream s2 uses subcarriers #1 to #M in thefrequency domain. Therefore, when streams s1 and s2 both have a symbolin the same subcarrier and at the same time, symbols of the two streamsare present at the same frequency. In the case where precoding performedincludes the precoding according to the scheme for regularly hoppingbetween precoding matrices as described in the other embodiments,streams s1 and s2 are subjected to weighting performed using theprecoding matrices and z1 and z2 are output from the respectiveantennas.

As shown in FIG. 64, in interval 1, a symbol group 6401 of PLP #1 istransmitted using streams s1 and s2, and the data transmission iscarried out using the spatial multiplexing MIMO system shown in FIG. 49or the MIMO system with a fixed precoding matrix.

In interval 2, a symbol group 6402 of PLP #2 is transmitted using streams1, and the data transmission is carried out by transmitting onemodulated signal.

In interval 3, a symbol group 6403 of PLP #3 is transmitted usingstreams s1 and s2, and the data transmission is carried out using aprecoding scheme of regularly hopping between precoding matrices.

In interval 4, a symbol group 6404 of PLP #4 is transmitted usingstreams s1 and s2, and the data transmission is carried out using thespace-time block coding shown in FIG. 50. Note that the symbolarrangement used in the space-time block coding is not limited to thearrangement in the time domain. Alternatively, the symbol arrangementmay be in the frequency domain or in symbol groups formed in the timeand frequency domains. In addition, the space-time block coding is notlimited to the one shown in FIG. 50.

In the case where a broadcast station transmits PLPs in the framestructure shown in FIG. 64, a reception device receiving thetransmission signal shown in FIG. 64 needs to know the transmissionscheme used for each PLP. As has been already described above, it istherefore necessary to transmit information indicating the transmissionscheme for each PLP, using the first and second Signalling data. Thefollowing describes an example of the scheme of structuring a P1 symbolused herein and the scheme of structuring first and second Signallingdata used herein. Specific examples of control information transmittedusing a P1 symbol are as shown in Table 3.

According to the DVB-T2 standard, the control information S1 (threebits) enables the reception device to determine whether or not theDVB-T2 standard is used and also determine, if DVB-T2 is used, thetransmission scheme used. If the three bits are set to “000”, the S1information indicates that the modulated signal transmitted is incompliant with “transmission of a modulated signal compliant with theDVB-T2 standard”.

If the three bits are set to “001”, the S1 information indicates thatthe modulated signal transmitted is in compliant with “transmissionusing space-time block coding compliant with the DVB-T2 standard”.

In the DVB-T2 standard, the bit sets “010” to “111” are “Reserved” forfuture use. In order to adapt the present invention in a manner toestablish compatibility with the DVB-T2, the three bits constituting theS1 information may be set to “010” (or any bit set other than “000” and“001”) to indicate that the modulated signal transmitted is compliantwith a standard other than DVB-T2. On determining that the S1information received is set to “010”, the reception device is informedthat the modulated signal transmitted from the broadcast station iscompliant with a standard other than DVB-T2.

Next, a description is given of examples of the scheme of structuringfirst and second Signalling data in the case where a modulated signaltransmitted by the broadcast station is compliant with a standard otherthan DVB-T2. A first example of the control information for the firstand second Signalling data is as shown in Table 4.

The 2-bit information “PLP_MODE” shown in Table 4 is control informationused to indicate the transmission scheme used for each PLP as shown inFIG. 64 (PLPs #1 to #4 in FIG. 64). That is, a separate piece of“PLP_MODE” information is provided for each PLP. That is, in the exampleshown in FIG. 64, PLP_MODE for PLP #1, PLP_MODE for PLP #2, PLP_MODE forPLP #3, PLP_MODE for PLP #4 . . . are transmitted from the broadcaststation. As a matter of course, by demodulating (and also performingerror correction) those pieces of information, the terminal at thereceiving end is enabled to recognize the transmission scheme that thebroadcast station used for transmitting each PLP.

With the PLP_MODE set to “00”, the data transmission by a correspondingPLP is carried out by “transmitting one modulated signal”. When thePLP_MODE is set to “01”, the data transmission by a corresponding PLP iscarried out by “transmitting a plurality of modulated signals obtainedby space-time block coding”. When the PLP_MODE is set to “10”, the datatransmission by a corresponding PLP is carried out using a “precodingscheme of regularly hopping between precoding matrices”. When thePLP_MODE is set to “11”, the data transmission by a corresponding PLP iscarried out using a “MIMO system with a fixed precoding matrix orspatial multiplexing MIMO system”.

Note that when the PLP_MODE is set to “01” to “11”, the informationindicating the specific processing conducted by the broadcast station(for example, the specific hopping scheme used in the scheme ofregularly hopping between precoding matrices, the specific space-timeblock coding scheme used, and the structure of precoding matrices used)needs to be notified to the terminal. The following describes the schemeof structuring control information that includes such information andthat is different from the example shown in Table 4.

A second example of the control information for the first and secondSignalling data is as shown in Table 5.

As shown in Table 5, the control information includes “PLP_MODE” whichis one bit long, “MIMO_MODE” which is one bit long, “MIMO_PATTERN #1”which is two bits long, and “MIMO_PATTERN #2” which is two bits long. Asshown in FIG. 64, these four pieces of control information is to notifythe transmission scheme of a corresponding one of PLPs (PLPs #1 to #4 inthe example shown in FIG. 64). Thus, a set of four pieces of informationis provided for each PLP. That is, in the example shown in FIG. 64, thebroadcast station transmits a set of PLP_MODE information, MIMO_MODEinformation, MIMO_PATTERN #1 information, and MIMO_PATTERN #2information for PLP #1, a set of PLP_MODE information, MIMO_MODEinformation, MIMO_PATTERN #1 information, and MIMO_PATTERN #2information for PLP #2, a set of PLP_MODE information, MIMO_MODEinformation, MIMO_PATTERN #1 information, and MIMO_PATTERN #2information for PLP #3, a set of PLP_MODE information, MIMO_MODEinformation, MIMO_PATTERN #1 information, and MIMO_PATTERN #2information for PLP #4 . . . . As a matter of course, by demodulating(and also performing error correction) those pieces of information, theterminal at the receiving end is enabled to recognize the transmissionscheme that the broadcast station used for transmitting each PLP.

With the PLP_MODE set to “0”, the data transmission by a correspondingPLP is carried out by “transmitting one modulated signal”. With thePLP_MODE set to “1”, the data transmission by a corresponding PLP iscarried out by “transmitting a plurality of modulated signals obtainedby space-time block coding”, “precoding scheme of regularly hoppingbetween precoding matrices”, “MIMO system with a fixed precoding matrixor spatial multiplexing MIMO system”, or “spatial multiplexing MIMOsystem”.

With the “PLP_MODE” set to “1”, the “MIMO_MODE” information is madeeffective. With “MIMO_MODE” set to “0”, data transmission is carried outby a scheme other than the “precoding scheme of regularly hoppingbetween precoding matrices”. With “MIMO_MODE” set to “1”, on the otherhand, data transmission is carried out by the “precoding scheme ofregularly hopping between precoding matrices”.

With “PLP_MODE” set to “1” and “MIMO_MODE” set to “0”, the “MIMO_PATTERN#1” information is made effective. With “MIMO_PATTERN #1” set to “00”,data transmission is carried out using space-time block coding. With“MIMO_PATTERN” set to “01”, data transmission is carried out using aprecoding scheme in which weighting is performed using a fixed precodingmatrix #1. With “MIMO_PATTERN” set to “10”, data transmission is carriedout using a precoding scheme in which weighting is performed using afixed precoding matrix #2 (Note that the precoding matrix #1 andprecoding matrix #2 are mutually different). When “MIMO_PATTERN” set to“11”, data transmission is carried out using spatial multiplexing MIMOsystem (Naturally, it may be construed that Scheme 1 shown in FIG. 49 isselected here).

With “PLP_MODE” set to “1” and “MIMO_MODE” set to “1”, the “MIMO_PATTERN#2” information is made effective. With “MIMO_PATTERN #2” set to “00”,data transmission is carried out using the precoding matrix hoppingscheme #1 according to which precoding matrices are regularly hopped.With “MIMO_PATTERN #2” set to “01”, data transmission is carried outusing the precoding matrix hopping scheme #2 according to whichprecoding matrices are regularly hopped. With “MIMO_PATTERN #3” set to“10”, data transmission is carried out using the precoding matrixhopping scheme #2 according to which precoding matrices are regularlyhopped. With “MIMO_PATTERN #4” set to “11”, data transmission is carriedout using the precoding matrix hopping scheme #2 according to whichprecoding matrices are regularly hopped. Note that the precoding matrixhopping schemes #1 to #4 are mutually different. Here, to define ascheme being different, it is supposed that #A and #B are mutuallydifferent schemes. Then one of the following is true.

-   -   The precoding matrices used in #A include the same matrices used        in #B but the periods (cycles) of the matrices are different.    -   The precoding matrices used in #A include precoding matrices not        used in #B.    -   None of the precoding matrices used in #A is used in #B.

In the above description, the control information shown in Tables 4 and5 is transmitted by first and second Signalling data. In this case, theadvantage of eliminating the need to specifically use PLPs to transmitcontrol information is achieved.

As described above, the present embodiment allows for choice of a schemeof regularly hopping between precoding matrices while using amulti-carrier scheme, such as an OFDM scheme and while allowing astandard other than DVB-T2 to be distinguished from DVB-T2. This offersthe advantages of obtaining high reception quality, as well as hightransmission speed, in an LOS environment. While in the presentembodiment, the transmission schemes to which a carrier group can be setare “a spatial multiplexing MIMO system, a MIMO scheme using a fixedprecoding matrix, a MIMO scheme for regularly hopping between precodingmatrices, space-time block coding, or a transmission scheme fortransmitting only stream s1”, but the transmission schemes are notlimited in this way. Furthermore, the MIMO scheme using a fixedprecoding matrix limited to scheme #2 in FIG. 49, as any structure witha fixed precoding matrix is acceptable.

Furthermore, the above description is directed to a scheme in which theschemes selectable by the broadcast station are “a spatial multiplexingMIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO schemefor regularly hopping between precoding matrices, space-time blockcoding, or a transmission scheme for transmitting only stream s1”.However, it is not necessary that all of the transmission schemes areselectable. Any of the following examples is also possible.

-   -   A transmission scheme in which any of the following is        selectable: a MIMO scheme using a fixed precoding matrix, a MIMO        scheme for regularly hopping between precoding matrices,        space-time block coding, and a transmission scheme for        transmitting only stream s1.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme using a fixed precoding matrix, a MIMO        scheme for regularly hopping between precoding matrices, and        space-time block coding.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme using a fixed precoding matrix, a MIMO        scheme for regularly hopping between precoding matrices, and a        transmission scheme for transmitting only stream s1.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme for regularly hopping between        precoding matrices, space-time block coding, and a transmission        scheme for transmitting only stream s1.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme using a fixed precoding matrix, and a        MIMO scheme for regularly hopping between precoding matrices.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme for regularly hopping between        precoding matrices, and space-time block coding.    -   A transmission scheme in which any of the following is        selectable: a MIMO scheme for regularly hopping between        precoding matrices, and a transmission scheme for transmitting        only stream s1.

As listed above, as long as a MIMO scheme for regularly hopping betweenprecoding matrices is included as a selectable scheme, the advantageouseffects of high-speed data transmission is obtained in an LOSenvironment, in addition to excellent reception quality for thereception device.

Here, it is necessary to set the control information S1 in P1 symbols asdescribed above. In addition, as first and second Signalling data, thecontrol information may be set differently from a scheme (the scheme forsetting the transmission scheme of each PLP) shown in Table 4. Table 6shows one example of such a scheme.

Table 6 differs from Table 4 in that the “PLP_MODE” set to “11” is“Reserved” In this way, the number of bits constituting the “PLP_MODE”shown in Tables 4 and 6 may be increased or decreased depending on thenumber of selectable PLP transmission schemes, which varies as in theexamples listed above.

The same holds with respect to Table 5. For example, if the only MIMOscheme supported is a precoding scheme of regularly hopping betweenprecoding matrices, the control information “MIMO_MODE” is no longernecessary. Furthermore, the control information “MIMO_PATTERN #1” maynot be necessary in the case, for example, where a MIMO scheme using afixed precoding matrix is not supported. Furthermore, the controlinformation “MIMO_PATTERN #1” may not necessarily be two bits long andmay alternatively be one bit long in the case where, for example, nomore than one precoding matrix is required for such a MIMO scheme usinga fixed precoding matrix. Furthermore, the control information“MIMO_PATTERN #1” may be two bits long or more in the case where aplurality of precoding matrices are selectable.

The same applies to “MIMO_PATTERN #2”. That is, the control information“MIMO_PATTERN #2” may be one bit long instead of two bits long, in thecase where no more than one precoding scheme of regularly hoppingbetween precoding matrices is available. Alternatively, the controlinformation “MIMO_PATTERN #2” may be two bits long or more in the casewhere a plurality of precoding schemes of regularly hopping betweenprecoding matrices are selectable.

In the present embodiment, the description is directed to thetransmission device having two antennas, but the number of antennas isnot limited to two. With a transmission device having more than twoantennas, the control information may be transmitted in the same manner.Yet, to enable the modulated signal transmission with the use of fourantennas in addition to the modulated signal transmission with the useof two antennas may require that the number of bits constitutingrespective pieces of control information needs to be increased. In sucha modification, it still holds that the control information istransmitted by the P1 symbol and the control information is transmittedby first and second Signalling data as set forth above.

The above description is directed to the frame structure of PLP symbolgroups transmitted by a broadcast station in a time-sharing transmissionscheme as shown in FIG. 64.

FIG. 66 shows another example of a symbol arranging scheme in the timeand frequency domains, which is different from the symbol arrangingscheme shown in FIG. 64. The symbols shown in FIG. 66 are of the streams1 and s2 and to be transmitted after the transmission of the P1 symbol,first and second Signalling data, and Common PLP.

In FIG. 66, each symbol denoted by “#1” represents one symbol of thesymbol group of PLP #1 shown in FIG. 67. Similarly, each symbol denotedas “#2” represents one symbol of the symbol group of PLP #2 shown inFIG. 64, each symbol denoted as “#3” represents one symbol of the symbolgroup of PLP #3 shown in FIG. 64, and each symbol denoted as “#4”represents one symbol of the symbol group of PLP #4 shown in FIG. 64.Similarly to FIG. 64, PLP #1 transmits data using spatial multiplexingMIMO system shown in FIG. 49 or the MIMO system with a fixed precodingmatrix. In addition, PLP #2 transmits data thereby to transmit onemodulated signal. PLP #3 transmits data using a precoding scheme ofregularly hopping between precoding matrices. PLP #4 transmits datausing space-time block coding shown in FIG. 50. Note that the symbolarrangement used in the space-time block coding is not limited to thearrangement in the time domain. Alternatively, the symbol arrangementmay be in the frequency domain or in symbol groups formed in the timeand frequency domains. In addition, the space-time block coding is notlimited to the one shown in FIG. 50.

In FIG. 66, where streams s1 and s2 both have a symbol in the samesubcarrier and at the same time, symbols of the two streams are presentat the same frequency. In the case where precoding performed includesthe precoding according to the scheme for regularly hopping betweenprecoding matrices as described in the other embodiments, streams s1 ands2 are subjected to weighting performed using the precoding matrices andz1 and z2 are output from the respective antennas.

FIG. 66 differs from FIG. 64 in the following points. That is, theexample shown in FIG. 64 is an arrangement of a plurality of PLPs usingtime-sharing, whereas the example shown in FIG. 66 is an arrangement ofa plurality of PLPs using both time-sharing and frequency-sharing. Thatis, for example, at time 1, a symbol of PLP #1 and a symbol of PLP #2are both present. Similarly, at time 3, a symbol of PLP #3 and a symbolof PLP #4 are both present. In this way, PLP symbols having differentindex numbers (#X; λ=1, 2 . . . ) may be allocated on a symbol-by-symbolbasis (for each symbol composed of one subcarrier per time).

For the sake of simplicity, FIG. 66 only shows symbols denoted by “#1”and “#2” at time 1. However, this is not a limiting example, and PLPsymbols having any index numbers other than “#1” and “#2” may be presentat time 1. In addition, the relation between subcarriers present at time1 and PLP index numbers are not limited to that shown in FIG. 66.Alternatively, a PLP symbol having any index number may be allocated toany subcarrier. Similarly, in addition, a PLP symbol having any indexnumber may be allocated to any subcarrier at any time other than time 1.

FIG. 67 shows another example of a symbol arranging scheme in the timeand frequency domains, which is different from the symbol arrangingscheme shown in FIG. 64. The symbols shown in FIG. 67 are of the streams1 and s2 and to be transmitted after the transmission of the P1 symbol,first and second Signalling data, and Common PLP. The characterizingfeature of the example shown in FIG. 67 is that the “transmission schemefor transmitting only stream s1” is not selectable in the case where PLPtransmission for T2 frames is carried out basically with a plurality ofantennas.

Therefore, data transmission by the symbol group 6701 of PLP #1 shown inFIG. 67 is carried out by “a spatial multiplexing MIMO system or a MIMOscheme using a fixed precoding matrix”. Data transmission by the symbolgroup 6702 of PLP #2 is carried out using “a precoding scheme ofregularly hopping between precoding matrices”. Data transmission by thesymbol group 6703 of PLP #3 is carried out by “space-time block coding”.Note that data transmission by the PLP symbol group 6703 of PLP #3 andthe following symbol groups in unit frame is carried out by using one of“a spatial multiplexing MIMO system or a MIMO scheme using a fixedprecoding matrix,” “a precoding scheme of regularly hopping betweenprecoding matrices” and “space-time block coding”.

FIG. 68 shows another example of a symbol arranging scheme in the timeand frequency domains, which is different from the symbol arrangingscheme shown in FIG. 66. The symbols shown in FIG. 68 are of the streams1 and s2 and to be transmitted after the transmission of the P1 symbol,first and second Signalling data, and Common PLP.

In FIG. 68, each symbol denoted by “#1” represents one symbol of thesymbol group of PLP #1 shown in FIG. 67. Similarly, each symbol denotedas “#2” represents one symbol of the symbol group of PLP #2 shown inFIG. 67, each symbol denoted as “#3” represents one symbol of the symbolgroup of PLP #3 shown in FIG. 67, and each symbol denoted as “#4”represents one symbol of the symbol group of PLP #4 shown in FIG. 67.Similarly to FIG. 67, PLP #1 transmits data using spatial multiplexingMIMO system shown in FIG. 49 or the MIMO system with a fixed precodingmatrix. PLP #2 transmits data using a precoding scheme of regularlyhopping between precoding matrices. PLP #3 transmits data usingspace-time block coding shown in FIG. 50. Note that the symbolarrangement used in the space-time block coding is not limited to thearrangement in the time domain. Alternatively, the symbol arrangementmay be in the frequency domain or in symbol groups formed in the timeand frequency domains. In addition, the space-time block coding is notlimited to the one shown in FIG. 50.

In FIG. 68, where streams s1 and s2 both have a symbol in the samesubcarrier and at the same time, symbols of the two streams are presentat the same frequency. In the case where precoding performed includesthe precoding according to the scheme for regularly hopping betweenprecoding matrices as described in the other embodiments, streams s1 ands2 are subjected to weighting performed using the precoding matrices andz1 and z2 are output from the respective antennas.

FIG. 68 differs from FIG. 67 in the following points. That is, theexample shown in FIG. 67 is an arrangement of a plurality of PLPs usingtime-sharing, whereas the example shown in FIG. 68 is an arrangement ofa plurality of PLPs using both time-sharing and frequency-sharing. Thatis, for example, at time 1, a symbol of PLP #1 and a symbol of PLP #2are both present. In this way, PLP symbols having different indexnumbers (#X; X=1, 2 . . . ) may be allocated on a symbol-by-symbol basis(for each symbol composed of one subcarrier per time).

For the sake of simplicity, FIG. 68 only shows symbols denoted by “#1”and “#2” at time 1. However, this is not a limiting example, and PLPsymbols having any index numbers other than “#1” and “#2” may be presentat time 1. In addition, the relation between subcarriers present at time1 and PLP index numbers are not limited to that shown in FIG. 68.Alternatively, a PLP symbol having any index number may be allocated toany subcarrier. Similarly, in addition, a PLP symbol having any indexnumber may be allocated to any subcarrier at any time other than time 1.Alternatively, on the other hand, only one PLP symbol may be allocatedat a specific time as at time t3. That is, in a framing scheme ofarranging PLP symbols in the time and frequency domains, any allocationis applicable.

As set forth above, no PLPs using “a transmission scheme fortransmitting only stream s1” exist in a unit frame, so that the dynamicrange of a signal received by the terminal is ensured to be narrow. As aresult, the advantageous effect is achieved that the probability ofexcellent reception quality increases.

Note that the description of FIG. 68 is described using an example inwhich the transmission scheme selected is one of “spatial multiplexingMIMO system or a MIMO scheme using a fixed precoding matrix”, “aprecoding scheme of regularly hopping between precoding matrices”, and“space-time block coding”. Yet, it is not necessary that all of thesetransmission schemes are selectable. For example, the followingcombinations of the transmission schemes may be made selectable.

-   -   A “precoding scheme of regularly hopping between precoding        matrices”, “space-time block coding”, and “MIMO scheme using a        fixed precoding matrix” are selectable.    -   A “precoding scheme of regularly hopping between precoding        matrices” and “space-time block coding” are selectable.    -   A “precoding scheme of regularly hopping between precoding        matrices” and “MIMO scheme using a fixed precoding matrix” are        selectable.

The above description relates to an example in which a unit frameincludes a plurality of PLPs. The following describes an example inwhich a unit frame includes one PLP only.

FIG. 69 shows an example of frame structure in the time and frequencydomains for stream s1 and s2 in the case where only one PLP exits in aunit frame.

In FIG. 69, the denotation “control symbol” represents a symbol such asP1 symbol, first and second Signalling data, or the like. In the exampleshown in FIG. 69, the first unit frame is transmitted using interval 1.Similarly, the second unit frame is transmitted using interval 2, thethird unit frame is transmitted using interval 3, and the fourth unitframe is transmitted using interval 4.

In the example shown in FIG. 69, in the first unit frame, a symbol group6801 for PLP #1-1 is transmitted and the transmission scheme selected is“spatial multiplexing MIMO system or MIMO scheme using a fixed precodingmatrix”.

In the second unit frame, a symbol group 6802 for PLP #2-1 istransmitted and the transmission scheme selected is “a scheme fortransmitting one modulated signal.”

In the third unit frame, a symbol group 6803 for PLP #3-1 is transmittedand the transmission scheme selected is “a precoding scheme of regularlyhopping between precoding matrices”.

In the fourth unit frame, a symbol group 6804 for PLP #4-1 istransmitted and the transmission scheme selected is “space-time blockcoding”. Note that the symbol arrangement used in the space-time blockcoding is not limited to the arrangement in the time domain.Alternatively, the symbols may be arranged in the frequency domain or insymbol groups formed in the time and frequency domains. In addition, thespace-time block coding is not limited to the one shown in FIG. 50.

In FIG. 69, where streams s1 and s2 both have a symbol in the samesubcarrier and at the same time, symbols of the two streams are presentat the same frequency. In the case where precoding performed includesthe precoding according to the scheme for regularly hopping betweenprecoding matrices as described in the other embodiments, streams s1 ands2 are subjected to weighting performed using the precoding matrices andz1 and z2 are output from the respective antennas.

In the above manner, a transmission scheme may be set for each PLP inconsideration of the data transmission speed and the data receptionquality at the receiving terminal, so that increase in data transmissionseeped and excellent reception quality are both achieved. As an examplescheme of structuring control information, the control informationindicating, for example, the transmission scheme and other informationof the P1 symbol and first and second Signalling data may be configuredin a similar manner to Tables 3-6. The difference is as follows. In theframe structure shown, for example, in FIG. 64, one unit frame includesa plurality of PLPs. Thus, it is necessary to provide the controlinformation indicating the transmission scheme and the like for eachPLP. On the other hand, in the frame structure shown, for example, inFIG. 69, one unit frame includes one PLP only. Thus, it is sufficient toprovide the control information indicating the transmission scheme andthe like only for the one PLP.

The present embodiment has described how a precoding scheme of regularlyhopping between precoding matrices is applied to a system compliant withthe DVB standard. Embodiments 1 to 16 have described examples of theprecoding scheme of regularly hopping between precoding matrices.However, the scheme of regularly hopping between precoding matrices isnot limited to the schemes described in Embodiments 1 to 16. The presentembodiment can be implemented in the same manner by using a schemecomprising the steps of (i) preparing a plurality of precoding matrices,(ii) selecting, from among the prepared plurality of precoding matrices,one precoding matrix for each slot, and (iii) performing the precodingwhile regularly hopping between precoding matrices to be used for eachslot.

Although control information has unique names in the present embodiment,the names of the control information do not influence the presentinvention.

Embodiment A2

The present embodiment provides detailed descriptions of a receptionscheme and the structure of a reception device used in a case where ascheme of regularly hopping between precoding matrices is applied to acommunication system compliant with the DVB-T2 standard, which isdescribed in Embodiment A1.

FIG. 73 shows, by way of example, the structure of a reception device ofa terminal used in a case where the transmission device of the broadcaststation shown in FIG. 63 has adopted a scheme of regularly hoppingbetween precoding matrices. In FIG. 73, the elements that operate in thesame manner as in FIGS. 7 and 56 have the same reference signs thereas.

Referring to FIG. 73, a P1 symbol detection/demodulation unit 7301performs signal detection and temporal frequency synchronization byreceiving a signal transmitted by a broadcast station and detecting a P1symbol based on the inputs, namely signals 704_X and 704_Y that havebeen subjected to signal processing. The P1 symboldetection/demodulation unit 7301 also obtains control informationincluded in the P1 symbol (by applying demodulation and error correctiondecoding) and outputs P1 symbol control information 7302. The P1 symbolcontrol information 7302 is input to OFDM related processors 5600_X and5600_Y. Based on the input information, the OFDM related processors5600_X and 5600_Y change a signal processing scheme for the OFDM scheme(this is because, as described in Embodiment A1, the P1 symbol includesinformation on a scheme for transmitting the signal transmitted by thebroadcast station).

Signals 704_X and 704_Y that have been subjected to signal processing,as well as the P1 symbol control information 7302, are input to a P2symbol demodulation unit 7303 (note, a P2 symbol may include asignalling PLP). The P2 symbol demodulation unit 7303 performs signalprocessing and demodulation (including error correction decoding) basedon the P1 symbol control information, and outputs P2 symbol controlinformation 7304.

The P1 symbol control information 7302 and the P2 symbol controlinformation 7304 are input to a control signal generating unit 7305. Thecontrol signal generating unit 7305 forms a set of pieces of controlinformation (relating to receiving operations) and outputs the same as acontrol signal 7306. As illustrated in FIG. 73, the control signal 7306is input to each unit.

A signal processing unit 711 receives, as inputs, the signals 706_1,706_2, 708_1, 708_2, 704_X, 704_Y, and the control signal 7306. Based onthe information included in the control signal 7306 on the transmissionscheme, modulation scheme, error correction coding scheme, coding ratefor error correction coding, block size of error correction codes, andthe like used to transmit each PLP, the signal processing unit 711performs demodulation processing and decoding processing, and outputsreceived data 712.

Here, the signal processing unit 711 may perform demodulation processingby using Equation 41 of Math 41 and Equation 143 of Math 153 in a casewhere any of the following transmission schemes is used for to transmiteach PLP: a spatial multiplexing MIMO system; a MIMO scheme employing afixed precoding matrix; and a precoding scheme of regularly hoppingbetween precoding matrices. Note that the channel matrix (H) can beobtained from the resultant outputs from channel fluctuation estimatingunits (705_1, 705_2, 707_1 and 707_2). The matrix structure of theprecoding matrix (F or W) differs depending on the transmission schemeactually used. Especially, when the precoding scheme of regularlyhopping between precoding matrices is used, the precoding matrices to beused are hopped between and demodulation is performed every time. Also,when space-time block coding is used, demodulation is performed by usingvalues obtained from channel estimation and a received (baseband)signal.

FIG. 74 shows, by way of example, the structure of a reception device ofa terminal used in a case where the transmission device of the broadcaststation shown in FIG. 72 has adopted a scheme of regularly hoppingbetween precoding matrices. In FIG. 74, the elements that operate in thesame manner as in FIGS. 7, 56 and 73 have the same reference signsthereas.

The reception device shown in FIG. 74 and the reception device shown inFIG. 73 are different in that the reception device shown in FIG. 73 canobtain data by receiving signals conforming to the DVB-T2 standard andsignals conforming to standards other than the DVB-T2 standard, whereasthe reception device shown in FIG. 74 can obtain data by receiving onlysignals conforming to standards other than the DVB-T2 standard.Referring to FIG. 74, a P1 symbol detection/demodulation unit 7301performs signal detection and temporal frequency synchronization byreceiving a signal transmitted by a broadcast station and detecting a P1symbol based on the inputs, namely signals 704_X and 704_Y that havebeen subjected to signal processing. The P1 symboldetection/demodulation unit 7301 also obtains control informationincluded in the P1 symbol (by applying demodulation and error correctiondecoding) and outputs P1 symbol control information 7302. The P1 symbolcontrol information 7302 is input to OFDM related processors 5600_X and5600_Y. Based on the input information, the OFDM related processors5600_X and 5600_Y change a signal processing scheme for the OFDM scheme.(This is because, as described in Embodiment A1h, the P1 symbol includesinformation on a scheme for transmitting the signal transmitted by thebroadcast station.) Signals 704_X and 704_Y that have been subjected tosignal processing, as well as the P1 symbol control information 7302,are input to a first/second signalling data demodulation unit 7401. Thefirst/second signalling data demodulation unit 7401 performs signalprocessing and demodulation (including error correction decoding) basedon the P1 symbol control information, and outputs first/secondsignalling data control information 7402.

The P1 symbol control information 7302 and the first/second signallingdata control information 7402 are input to a control signal generatingunit 7305. The control signal generating unit 7305 forms a set of piecesof control information (relating to receiving operations) and outputsthe same as a control signal 7306. As illustrated in FIG. 74, thecontrol signal 7306 is input to each unit.

A signal processing unit 711 receives, as inputs, the signals 706_1,706_2, 708_1, 708_2, 704_X, 704_Y, and the control signal 7306. Based onthe information included in the control signal 7306 on the transmissionscheme, modulation scheme, error correction coding scheme, coding ratefor error correction coding, block size of error correction codes, andthe like used to transmit each PLP, the signal processing unit 711performs demodulation processing and decoding processing, and outputsreceived data 712.

Here, the signal processing unit 711 may perform demodulation processingby using Equation 41 of Math 41 and Equation 143 of Math 153 in a casewhere any of the following transmission schemes is used to transmit eachPLP: a spatial multiplexing MIMO system; a MIMO scheme employing a fixedprecoding matrix; and a precoding scheme of regularly hopping betweenprecoding matrices. Note that the channel matrix (H) can be obtainedfrom the resultant outputs from channel fluctuation estimating units(705_1, 705_2, 707_1 and 707_2). The matrix structure of the precodingmatrix (F or W) differs depending on the transmission scheme actuallyused. Especially, when the precoding scheme of regularly hopping betweenprecoding matrices is used, the precoding matrices to be used are hoppedbetween and demodulation is performed every time. Also, when space-timeblock coding is used, demodulation is performed by using values obtainedfrom channel estimation and a received (baseband) signal.

FIG. 75 shows the structure of a reception device of a terminalcompliant with both the DVB-T2 standard and standards other than theDVB-T2 standard. In FIG. 75, the elements that operate in the samemanner as in FIGS. 7, 56 and 73 have the same reference signs thereas.

The reception device shown in FIG. 75 is different from the receptiondevices shown in FIGS. 73 and 74 in that the reception device shown inFIG. 75 comprises a P2 symbol or first/second signalling datademodulation unit 7501 so as to be able to demodulate both signalscompliant with the DVB-T2 standard and signals compliant with standardsother than the DVB-T2 standard.

Signals 704_X and 704_Y that have been subjected to signal processing,as well as P1 symbol control information 7302, are input to the P2symbol or first/second signalling data demodulation unit 7501. Based onthe P1 symbol control information, the P2 symbol or first/secondsignalling data demodulation unit 7501 judges whether the receivedsignal is compliant with the DVB-T2 standard or with a standard otherthan the DVB-T2 standard (this judgment can be made with use of, forexample, Table 3), performs signal processing and demodulation(including error correction decoding), and outputs control information7502 that includes information indicating the standard with which thereceived signal is compliant. Other operations are similar to FIGS. 73and 74.

As set forth above, the structure of the reception device described inthe present embodiment allows obtaining data with high reception qualityby receiving the signal transmitted by the transmission device of thebroadcast station, which has been described in Embodiment A1, and byperforming appropriate signal processing. Especially, when receiving asignal associated with a precoding scheme of regularly hopping betweenprecoding matrices, both the data transmission efficiency and the datareception quality can be improved in an LOS environment.

As the present embodiment has described the structure of the receptiondevice that corresponds to the transmission scheme used by the broadcaststation described in Embodiment A1, the reception device is providedwith two receive antennas in the present embodiment. However, the numberof antennas provided in the reception device is not limited to two. Thepresent embodiment can be implemented in the same manner when thereception device is provided with three or more antennas. In this case,the data reception quality can be improved due to an increase in thediversity gain. Furthermore, when the transmission device of thebroadcast station is provided with three or more transmit antennas andtransmits three or more modulated signals, the present embodiment can beimplemented in the same manner by increasing the number of receiveantennas provided in the reception device of the terminal. In this case,it is preferable that the precoding scheme of regularly hopping betweenprecoding matrices be used as a transmission scheme.

Note that Embodiments 1 to 16 have described examples of the precodingscheme of regularly hopping between precoding matrices. However, thescheme of regularly hopping between precoding matrices is not limited tothe schemes described in Embodiments 1 to 16. The present embodiment canbe implemented in the same manner by using a scheme comprising the stepsof (i) preparing a plurality of precoding matrices, (ii) selecting, fromamong the prepared plurality of precoding matrices, one precoding matrixfor each slot, and (iii) performing the precoding while regularlyhopping between precoding matrices to be used for each slot.

Embodiment A3

In the system described in Embodiment A1 where the precoding scheme ofregularly hopping between precoding matrices is applied to the DVB-T2standard, there is control information for designating a pilot insertionpattern in L1 pre-signalling. The present embodiment describes how toapply the precoding scheme of regularly hopping between precodingmatrices when the pilot insertion pattern is changed in the L1pre-signalling.

FIGS. 76A, 76B, 77A and 77B show examples of a frame structurerepresented in a frequency-time domain for the DVB-T2 standard in a casewhere a plurality of modulated signals are transmitted from a pluralityof antennas using the same frequency bandwidth. In each of FIGS. 76A to77B, the horizontal axis represents frequency and carrier numbers areshown therealong, whereas the vertical axis represents time. FIGS. 76Aand 77A each show a frame structure for a modulated signal z1 pertainingto the embodiments that have been described so far. FIGS. 76B and 77Beach show a frame structure for a modulated signal z2 pertaining to theembodiments that have been described so far. Indexes “f0, f1, f2, . . .” are assigned as carrier numbers, and indexes “t1, t2, t3, . . . ” areassigned as time. In FIGS. 76A to 77B, symbols that are assigned thesame carrier number and the same time exist over the same frequency atthe same time.

FIGS. 76A to 77B show examples of positions in which pilot symbols areinserted according to the DVB-T2 standard (when a plurality of modulatedsignals are transmitted by using a plurality of antennas according tothe DVB-T2, there are eight schemes regarding the positions in whichpilots are inserted; FIGS. 76A to 77B show two of such schemes). FIGS.76A to 77B show two types of symbols, namely, symbols as pilots andsymbols for data transmission (“data transmission symbols”). Asdescribed in other embodiments, when a precoding scheme of regularlyhopping between precoding matrices or a precoding scheme employing afixed precoding matrix is used, data transmission symbols in themodulated signal z1 are obtained as a result of performing weighting onthe streams s1 and s2, and data transmission symbols in the modulatedsignal z2 are obtained as a result of performing weighting on thestreams s1 and s2. When the space-time block coding or the spatialmultiplexing MIMO system is used, data transmission symbols in themodulated signal z1 are either for the stream s1 or for the stream s2,and data transmission symbols in the modulated signal z2 are either forthe stream s1 or for the stream s2.

In FIGS. 76A to 77B, the symbols as pilots are each assigned an index“PP1” or “PP2”. A pilot symbol with the index “PP1” and a pilot symbolwith the index “PP2” are structured by using different schemes. Asmentioned earlier, according to the DVB-T2 standard, the broadcaststation can designate one of the eight pilot insertion schemes (thatdiffer from one another in the frequency of insertion of pilot symbolsin a frame). FIGS. 76A to 77B show two of the eight pilot insertionschemes. Information on one of the eight pilot insertion schemesselected by the broadcast station is transmitted to a transmissiondestination (terminal) as L1 pre-signalling data of P2 symbols, whichhas been described in embodiment A1.

Next, a description is given of how to apply the precoding scheme ofregularly hopping between precoding matrices in association with a pilotinsertion scheme. By way of example, it is assumed here that 10different types of precoding matrices F are prepared for the precodingscheme of regularly hopping between precoding matrices, and these 10different types of precoding matrices F are expressed as F[0], F[1],F[2], F[3], F[4], F[5], F[6], F[7], F[8], and F[9]. FIGS. 78A and 78Bshow the result of allocating the precoding matrices to the framestructure represented in the frequency-time domains shown in FIGS. 76Aand 76B when the precoding scheme of regularly hopping between precodingmatrices is applied. FIGS. 79A and 79B show the result of allocating theprecoding matrices to the frame structure represented in thefrequency-time domains shown in FIGS. 77A and 77B when the precodingscheme of regularly hopping between precoding matrices is applied. Forexample, in both of the frame structure for the modulated signal z1shown in FIG. 78A and the frame structure for the modulated signal z2shown in FIG. 78B, a symbol at the carrier f1 and the time t1 shows“#1”. This means that precoding is performed on this symbol by using theprecoding matrix F[1]. Likewise, in FIGS. 78A to 79B, a symbol at thecarrier fx and the time ty showing “#Z” denotes that precoding isperformed on this symbol by using the precoding matrix F[Z] (here, x=0,1, 2, . . . , and y=1, 2, 3, . . . ).

It should be naturally appreciated that different schemes for insertingpilot symbols (different insertion intervals) are used for the framestructure represented in the frequency-time domain shown in FIGS. 78Aand 78B and the frame structure represented in the frequency-time domainshown in FIGS. 79A and 79B. Furthermore, the precoding scheme ofregularly hopping between the coding matrices is not applied to pilotsymbols. For this reason, even if all of the signals shown in FIGS. 78Ato 79B are subjected to the same precoding scheme that regularly hopsbetween precoding matrices over a certain period (cycle) (i.e., the samenumber of different precoding matrices are prepared for this schemeapplied to all of the signals shown in FIGS. 78A to 79B), a precodingmatrix allocated to a symbol at a certain carrier and a certain time inFIGS. 78A and 78B may be different from a precoding matrix allocated tothe corresponding symbol in FIGS. 79A and 79B. This is apparent fromFIGS. 78A to 79B. For example, in FIGS. 78A and 78B, a symbol at thecarrier f5 and the time t2 shows “#7”, meaning that precoding isperformed thereon by using the precoding matrix F[7]. On the other hand,in FIGS. 79A and 79B, a symbol at the carrier f5 and the time t2 shows“#8”, meaning that precoding is performed thereon by using the precodingmatrix F[8].

Therefore, the broadcast station transmits control informationindicating a pilot pattern (pilot insertion scheme) using the L1pre-signalling data. Note, when the broadcast station has selected theprecoding scheme of regularly hopping between precoding matrices as ascheme for transmitting each PLP based on control information shown inTable 4 or 5, the control information indicating the pilot pattern(pilot insertion scheme) may additionally indicate a scheme forallocating the precoding matrices (hereinafter “precoding matrixallocation scheme”) prepared for the precoding scheme of regularlyhopping between precoding matrices. Hence, the reception device of theterminal that receives modulated signals transmitted by the broadcaststation can acknowledge the precoding matrix allocation scheme used inthe precoding scheme of regularly hopping between precoding matrices byobtaining the control information indicating the pilot pattern, which isincluded in the L1 pre-signalling data (on the premise that thebroadcast station has selected the precoding scheme of regularly hoppingbetween precoding matrices as a scheme for transmitting each PLP basedon control information shown in Table 4 or 5). Although the descriptionof the present embodiment has been given with reference to L1pre-signalling data, in the case of the frame structure shown in FIG. 70where no P2 symbol exists, the control information indicating the pilotpattern and the precoding matrix allocation scheme used in the precodingscheme of regularly hopping between precoding matrices is included infirst signalling data and second signalling data.

The following describes another example. For example, the abovedescription is also true of a case where the precoding matrices used inthe precoding scheme of regularly hopping between precoding matrices aredetermined at the same time as designation of a modulation scheme, asshown in Table 2. In this case, by transmitting only the pieces ofcontrol information indicating a pilot pattern, a scheme fortransmitting each PLP and a modulation scheme from P2 symbols, thereception device of the terminal can estimate, via obtainment of thesepieces of control information, the precoding matrix allocation schemeused in the precoding scheme of regularly hopping between precodingmatrices (note, the allocation is performed in the frequency-timedomain). Assume a case where the precoding matrices used in theprecoding scheme of regularly hopping between precoding matrices aredetermined at the same time as designation of a modulation scheme and anerror correction coding scheme, as shown in Table 1B. In this case also,by transmitting only the pieces of control information indicating apilot pattern, a scheme for transmitting each PLP and a modulationscheme, as well as an error correction coding scheme, from P2 symbols,the reception device of the terminal can estimate, via obtainment ofthese pieces of information, the precoding matrix allocation scheme usedin the precoding scheme of regularly hopping between precoding matrices(note, the allocation is performed in the frequency-time domain).

However, unlike the cases of Tables 1B and 2, a precoding matrix hoppingscheme used in the precoding scheme of regularly hopping betweenprecoding matrices is transmitted, as indicated by Table 5, in any ofthe following situations (i) to (iii): (i) when one of two or moredifferent schemes of regularly hopping between precoding matrices can beselected even if the modulation scheme is determined (examples of suchtwo or more different schemes include: precoding schemes that regularlyhop between precoding matrices over different periods (cycles); andprecoding schemes that regularly hop between precoding matrices, wherethe precoding matrices used in one scheme is different from those usedin another; (ii) when one of two or more different schemes of regularlyhopping between precoding matrices can be selected even if themodulation scheme and the error correction scheme are determined; and(iii) when one of two or more different schemes of regularly hoppingbetween precoding matrices can be selected even if the error correctionscheme is determined. In any of these situations (i) to (iii), it ispermissible to transmit information on the precoding matrix allocationscheme used in the precoding scheme of regularly hopping betweenprecoding matrices, in addition to the precoding matrix hopping schemeused in the precoding scheme of regularly hopping between precodingmatrices (note, the allocation is performed in the frequency-timedomain).

Table 7 shows an example of the structure of control information for theinformation on the precoding matrix allocation scheme used in theprecoding scheme of regularly hopping between precoding matrices (note,the allocation is performed in the frequency-time domain).

TABLE 7 MATRIX_FRAME_ARRANGEMENT 00: Precoding matrix (2 bits)allocation scheme #1 in frames 01: Precoding matrix allocation scheme #2in frames 10: Precoding matrix allocation scheme #3 in frames 11:Precoding matrix allocation scheme #4 in frames

By way of example, assume a case where the transmission device of thebroadcast station has selected the pilot insertion pattern shown inFIGS. 76A and 76B, and selected a scheme A as the precoding scheme ofregularly hopping between precoding matrices. In this case, thetransmission device of the broadcast station can select either theprecoding matrix allocation scheme shown in FIGS. 78A and 78B or theprecoding matrix allocation scheme shown in FIGS. 80A and 80B (note, theallocation is performed in the frequency-time domain). For example, whenthe transmission device of the broadcast station has selected theprecoding matrix allocation scheme shown in FIGS. 78A and 78B,“MATRIX_FRAME_ARRANGEMENT” in Table 7 is set to “00”. On the other hand,when the transmission device has selected the precoding matrixallocation scheme shown in FIGS. 80A and 80B, “MATRIX_FRAME_ARRANGEMENT”in Table 7 is set to “01”. Then, the reception device of the terminalcan acknowledge the precoding matrix allocation scheme by obtaining thecontrol information shown in Table 7 (note, the allocation is performedin the frequency-time domain). Note that the control information shownin Table 7 can be transmitted by using P2 symbols, or by using firstsignalling data and second signalling data.

As set forth above, by implementing the precoding matrix allocationscheme used in the precoding scheme of regularly hopping betweenprecoding matrices based on the pilot insertion scheme, and by properlytransmitting the information indicative of the precoding matrixallocation scheme to the transmission destination (terminal), thereception device of the terminal can achieve the advantageous effect ofimproving both the data transmission efficiency and the data receptionquality.

The present embodiment has described a case where the broadcast stationtransmits two signals. However, the present embodiment can beimplemented in the same manner when the transmission device of thebroadcast station is provided with three or more transmit antennas andtransmits three or more modulated signals. Embodiments 1 to 16 havedescribed examples of the precoding scheme of regularly hopping betweenprecoding matrices. However, the scheme of regularly hopping betweenprecoding matrices is not limited to the schemes described inEmbodiments 1 to 16. The present embodiment can be implemented in thesame manner by using a scheme comprising the steps of (i) preparing aplurality of precoding matrices, (ii) selecting, from among the preparedplurality of precoding matrices, one precoding matrix for each slot, and(iii) performing the precoding while regularly hopping between precodingmatrices to be used for each slot.

Embodiment A4

In the present embodiment, a description is given of a repetition schemeused in a precoding scheme of regularly hopping between precodingmatrices in order to improve the data reception quality.

FIGS. 3, 4, 13, 40 and 53 each show the structure of a transmissiondevice employing the precoding scheme of regularly hopping betweenprecoding matrices. On the other hand, the present embodiment describesthe examples where repetition is used in the precoding scheme ofregularly hopping between precoding matrices.

FIG. 81 shows an example of the structure of the signal processing unitpertaining to a case where repetition is used in the precoding scheme ofregularly hopping between precoding matrices. In light of FIG. 53, thestructure of FIG. 81 corresponds to the signal processing unit 5308.

A baseband signal 8101_1 shown in FIG. 81 corresponds to the basebandsignal 5307_1 shown in FIG. 53. The baseband signal 8101_1 is obtainedas a result of mapping, and constitutes the stream s1. Likewise, abaseband signal 8101_2 shown in FIG. 81 corresponds to the basebandsignal 5307_2 shown in FIG. 53. The baseband signal 8101_2 is obtainedas a result of mapping, and constitutes the stream s2.

The baseband signal 8101_1 and a control signal 8104 are input to asignal processing unit (duplicating unit) 8102_1. The signal processingunit (duplicating unit) 8102_1 generates duplicates of the basebandsignal in accordance with the information on the number of repetitionsincluded in the control signal 8104. For example, in a case where theinformation on the number of repetitions included in the control signal8104 indicates four repetitions, provided that the baseband signal8101_1 includes signals s11, s12, s13, s14, . . . arranged in the statedorder along the time axis, the signal processing unit (duplicating unit)8102_1 generates a duplicate of each signal four times, and outputs theresultant duplicates. That is, after the four repetitions, the signalprocessing unit (duplicating unit) 8102_1 outputs, as the basebandsignal 8103_1, four pieces of s11 (i.e., s11, s11, s11, s11), fourpieces of s12 (i.e., s12, s12, s12, s12), four pieces of s13 (i.e., s13,s13, s13, s13), four pieces of s14 (i.e., s14, s14, s14, s14) and so on,in the stated order along the time axis.

The baseband signal 8101_2 and the control signal 8104 are input to asignal processing unit (duplicating unit) 8102_2. The signal processingunit (duplicating unit) 8102_2 generates duplicates of the basebandsignal in accordance with the information on the number of repetitionsincluded in the control signal 8104. For example, in a case where theinformation on the number of repetitions included in the control signal8104 indicates four repetitions, provided that the baseband signal8101_2 includes signals s21, s22, s23, s24, . . . arranged in the statedorder along the time axis, the signal processing unit (duplicating unit)8102_2 generates a duplicate of each signal four times, and outputs theresultant duplicates. That is, after the four repetitions, the signalprocessing unit (duplicating unit) 8102_2 outputs, as the basebandsignal 8103_2, four pieces of s21 (i.e., s21, s21, s21, s21), fourpieces of s22 (i.e., s22, s22, s22, s22), four pieces of s23 (i.e., s23,s23, s23, s13), four pieces of s24 (i.e., s14, s24, s24, s24) and so on,in the stated order along the time axis.

The baseband signals 8103_1 and 8103_2 obtained as a result ofrepetitions, as well as the control signal 8104, are input to aweighting unit (precoding operation unit) 8105. The weighting unit(precoding operation unit) 8105 performs precoding based on theinformation on the precoding scheme of regularly hopping betweenprecoding matrices, which is included in the control signal 8104. Morespecifically, the weighting unit (precoding operation unit) 8105performs weighting on the baseband signals 8103_1 and 8103_2 obtained asa result of repetitions, and outputs baseband signals 8106_1 and 8106_2on which the precoding has been performed (here, the baseband signals8106_1 and 8106_2 are respectively expressed as z1(i) and z2(i), where irepresents the order (along time or frequency)).

Provided that the baseband signals 8103_1 and 8103_2 obtained as aresult of repetitions are respectively y1(i) and y2(i) and the precodingmatrix is F(i), the following relationship is satisfied.

Math 561

$\begin{matrix}{\begin{pmatrix}{z\; 1(i)} \\{z\; 2(i)}\end{pmatrix} = {{F(i)}\begin{pmatrix}{y\; 1(i)} \\{y\; 2(i)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 475}\end{matrix}$

Provided that N precoding matrices prepared for the precoding scheme ofregularly hopping between precoding matrices are F[0], F[1], F[2], F[3],. . . , F[N−1] (where N is an integer larger than or equal to two), oneof the precoding matrices F[0], F[1], F[2], F[3], . . . , F[N−1] is usedas F(i) in Equation 475.

By way of example, assume that i=0, 1, 2, 3; y1(i) represents fourduplicated baseband signals s11, s11, s11, s11; and y2(i) representsfour duplicated baseband signals s21, s21, s21, s21. Under thisassumption, it is important that the following condition be met.

Math 562

For ^(∀)α^(∀)β, the relationship F(α)≠F(β) is satisfied (for α, β=0, 1,2, 3 and α≠β).

The following description is derived by generalizing the above. Assumethat the number of repetitions is K; i=g₀, g₁, g₂, . . . , g_(K-1)(i.e., g_(j) where j is an integer in a range of 0 to K−1); and y1(i)represents s11. Under this assumption, it is important that thefollowing condition be met.

Math 563

For ^(∀)α^(∀)β, the relationship F(α)≠F(β) is satisfied (for α, β=g_(j)(j being an integer in a range of 0 to K−1) and α≠β).

Likewise, assume that the number of repetitions is K; i=h₀, h₁, h₂, . .. , h_(K-1) (i.e., h_(j) where j is an integer in a range of 0 to K−1);and y2(i) represents s21. Under this assumption, it is important thatthe following condition be met.

Math 564

For ^(∀)α^(∀)β, the relationship F(α)≠F(β) is satisfied (for α, β=h_(j)(j being an integer in a range of 0 to K−1) and α≠β).

Here, the relationship g_(j)=h_(j) may be or may not be satisfied. Thisway, the identical streams generated through the repetitions aretransmitted while using different precoding matrices therefor, and thusthe advantageous effect of improving the data reception quality isachieved.

The present embodiment has described a case where the broadcast stationtransmits two signals. However, the present embodiment can beimplemented in the same manner when the transmission device of thebroadcast station is provided with three or more transmit antennas andtransmits three or more modulated signals. Assume that the number oftransmitted signals is Q; the number of repetitions is K; i=g₀, g₁, g₂,. . . , g_(K-1) (i.e., g_(j) where j is an integer in a range of 0 toK−1); and yb(i) represents sb1 (where b is an integer in a range of 1 toQ). Under this assumption, it is important that the following conditionbe met.

Math 565

For ^(∀)α^(∀)β, the relationship F(α)≠F(β) is satisfied (for α, β=g_(j)(j being an integer in a range of 0 to K−1) and α≠β).

Note that F(i) is a precoding matrix pertaining to a case where thenumber of transmitted signals is Q.

Next, an embodiment different from the embodiment illustrated in FIG. 81is described with reference to FIG. 82. In FIG. 82, the elements thatoperate in the same manner as in FIG. 81 have the same reference signsthereas. The structure shown in FIG. 82 is different from the structureshown in FIG. 81 in that data pieces are reorders so as to transmitidentical data pieces from different antennas.

A baseband signal 8101_1 shown in FIG. 82 corresponds to the basebandsignal 5307_1 shown in FIG. 53. The baseband signal 8101_1 is obtainedas a result of mapping, and constitutes the s1 stream. Similarly, abaseband signal 8101_2 shown in FIG. 81 corresponds to the basebandsignal 5307_2 shown in FIG. 53. The baseband signal 8101_2 is obtainedas a result of mapping, and constitutes the s2 stream.

The baseband signal 8101_1 and the control signal 8104 are input to asignal processing unit (duplicating unit) 8102_1. The signal processingunit (duplicating unit) 8102_1 generates duplicates of the basebandsignal in accordance with the information on the number of repetitionsincluded in the control signal 8104. For example, in a case where theinformation on the number of repetitions included in the control signal8104 indicates four repetitions, provided that the baseband signal8101_1 includes signals s11, s12, s13, s14, . . . arranged in the statedorder along the time axis, the signal processing unit (duplicating unit)8102_1 generates a duplicate of each signal four times, and outputs theresultant duplicates. That is, after the four repetitions, the signalprocessing unit (duplicating unit) 8102_1 outputs, as the basebandsignal 8103_1, four pieces of s11 (i.e., s1, s1, s1, s11), four piecesof s12 (i.e., s12, s12, s12, s12), four pieces of s13 (i.e., s13, s13,s13, s13), four pieces of s14 (i.e., s14, s14, s14, s14) and so on, inthe stated order along the time axis.

The baseband signal 8101_2 and the control signal 8104 are input to asignal processing unit (duplicating unit) 8102_2. The signal processingunit (duplicating unit) 8102_2 generates duplicates of the basebandsignal in accordance with the information on the number of repetitionsincluded in the control signal 8104. For example, in a case where theinformation on the number of repetitions included in the control signal8104 indicates four repetitions, provided that the baseband signal8101_2 includes signals s21, s22, s23, s24, . . . arranged in the statedorder along the time axis, the signal processing unit (duplicating unit)8102_1 generates a duplicate of each signal four times, and outputs theresultant duplicates. That is, after the four repetitions, the signalprocessing unit (duplicating unit) 8102_2 outputs, as the basebandsignal 8103_2, four pieces of s21 (i.e., s21, s21, s21, s21), fourpieces of s22 (i.e., s22, s22, s22, s22), four pieces of s23 (i.e., s23,s23, s23, s23), four pieces of s24 (i.e., s24, s24, s24, s24) and so on,in the stated order along the time axis.

The baseband signals 8103_1 and 8103_2 obtained as a result ofrepetitions, as well as the control signal 8104, are input to areordering unit 8201. The reordering unit 8201 reorders the data piecesin accordance with information on a repetition scheme included in thecontrol signal 8104, and outputs baseband signals 8202_1 and 8202_2obtained as a result of reordering. For example, assume that thebaseband signal 8103_1 obtained as a result of repetitions is composedof four pieces of s11 (s11, s1, s1, s1) arranged along the time axis,and the baseband signal 8103_2 obtained as a result of repetitions iscomposed of four pieces of s21 (s21, s21, s21, s21) arranged along thetime axis. In FIG. 82, s11 is output as both y1(i) and y2(i) of Equation475, and s21 is similarly output as both y1(i) and y2(i) of Equation475. Likewise, the reordering similar to the reordering performed on s11is performed on s12, s13, . . . , and the reordering similar to thereordering performed on s21 is performed on s22, s23, . . . . Hence, thebaseband signal 8202_1 obtained as a result of reordering includes s11,s21, s11, s21, s12, s22, s12, s22, s13, s23, s13, s23, . . . arranged inthe stated order, which are equivalent to y1(i) of Equation 475.Although the pieces of s11 and s21 are arranged in the order s11, s21,s11 and s21 in the above description, the pieces of s11 and s21 are notlimited to being arranged in this way, but may be arranged in any order.Similarly, the pieces of s12 and s22, as well as the pieces of s13 ands23, may be arranged in any order. The baseband signal 8202_2 obtainedas a result of reordering includes s21, s11, s21, s11, s22, s12, s22,s12, s23, s13, s23, s13, . . . in the stated order, which are equivalentto y2(i) of Equation 475. Although the pieces of s11 and s21 arearranged in the order s21, s11, s21 and s11 in the above description,the pieces of s11 and s21 are not limited to being arranged in this way,but may be arranged in any order. Similarly, the pieces of s12 and s22,as well as the pieces of s13 and s23, may be arranged in any order.

The baseband signals 8202_1 and 8202_2 obtained as a result ofreordering, as well as the control signal 8104, are input to a weightingunit (precoding operation unit) 8105. The weighting unit (precodingoperation unit) 8105 performs precoding based on the information on theprecoding scheme of regularly hopping between precoding matrices, whichis included in the control signal 8104. More specifically, the weightingunit (precoding operation unit) 8105 performs weighting on the basebandsignals 8202_1 and 8202_2 obtained as a result of reordering, andoutputs baseband signals 8106_1 and 8106_2 on which the precoding hasbeen performed (here, the baseband signals 8106_1 and 8106_2 arerespectively expressed as z1(i) and z2(i), where i represents the order(along time or frequency)).

As described earlier, under the assumption that the baseband signals8202_1 and 8202_2 obtained as a result of reordering are respectivelyy1(i) and y2(i) and the precoding matrix is F(i), the relationship inEquation 475 is satisfied.

Provided that N precoding matrices prepared for the precoding scheme ofregularly hopping between precoding matrices are F[0], F[1], F[2], F[3],. . . , F[N−1] (where N is an integer larger than or equal to two), oneof the precoding matrices F[0], F[1], F[2], F[3], . . . , F[N−1] is usedas F(i) in Equation 475.

Although it has been described above that four repetitions areperformed, the number of repetitions is not limited to four. As with thestructure shown in FIG. 81, the structure shown in FIG. 82 also achieveshigh reception quality when the relationships set out in Math 304 toMath 307 are satisfied.

The structure of the reception device is illustrated in FIGS. 7 and 56.By taking advantage of fulfillment of the relationships set out inEquation 144 and Equation 475, the signal processing unit demodulatesbits transmitted by each of s11, s12, s13, s14, . . . , and bitstransmitted by each of s21, s22, s23, s24, . . . . Note that each bitmay be calculated as a log-likelihood ratio or as a hard-decision value.Furthermore, by taking advantage of the fact that K repetitions areperformed on s11, it is possible to obtain highly reliable estimatevalues for bits transmitted by s1. Likewise, by taking advantage of thefact that K repetitions are performed on s12, s13, . . . , and on s21,s22, s23, . . . , it is possible to obtain highly reliable estimatevalues for bits transmitted by s12, s13, . . . , and by s21, s22, s23, .. . .

The present embodiment has described a scheme for applying a precodingscheme of regularly hopping between precoding matrices in the case wherethe repetitions are performed. When there are two types of slots, i.e.,slots over which data is transmitted after performing the repetitions,and slots over which data is transmitted without performing therepetitions, either of a precoding scheme of regularly hopping betweenprecoding matrices or a precoding scheme employing a fixed precodingmatrix may be used as a transmission scheme for the slots over whichdata is transmitted without performing the repetitions. Put another way,in order for the reception device to achieve high data receptionquality, it is important that the transmission scheme pertaining to thepresent embodiment be used for the slots over which data is transmittedafter performing the repetitions.

In the systems associated with the DVB standard that have been describedin Embodiments A1 through A3, it is necessary to secure higher receptionqualities for P2 symbols, first signalling data and second signallingdata than for PLPs. When P2 symbols, first signalling data and secondsignalling data are transmitted by using the precoding scheme ofregularly hopping between precoding matrices described in the presentembodiment, which incorporates the repetitions, the reception quality ofcontrol information improves in the reception device. This is importantfor stable operations of the systems.

Embodiments 1 to 16 have provided examples of the precoding scheme ofregularly hopping between precoding matrices described in the presentembodiment. However, the scheme of regularly hopping between precodingmatrices is not limited to the schemes described in Embodiments 1 to 16.The present embodiment can be implemented in the same manner by using ascheme comprising the steps of (i) preparing a plurality of precodingmatrices, (ii) selecting, from among the prepared plurality of precodingmatrices, one precoding matrix for each slot, and (iii) performing theprecoding while regularly hopping between precoding matrices for eachslot.

Embodiment A5

The present embodiment describes a scheme for transmitting modulatedsignals by applying common amplification to the transmission schemedescribed in Embodiment A1.

FIG. 83 shows an example of the structure of a transmission device. InFIG. 83, the elements that operate in the same manner as in FIG. 52 havethe same reference signs thereas.

Modulated signal generating units #1 to #M (i.e., 5201_1 to 5201_M)shown in FIG. 83 generate the signals 6323_1 and 6323_2 from the inputsignals (input data), the signals 6323_1 and 6323_2 being subjected toprocessing for a P1 symbol and shown in FIG. 63 or 72. The modulatedsignal generating units #1 to #M output modulated signals z1 (5202_1 to5202 _M) and modulated signals z2 (5203_1 to 5203_M).

The modulated signals z1 (5202_1 to 5202M) are input to a wirelessprocessing unit 8301_1 shown in FIG. 83. The wireless processing unit8301_1 performs signal processing (e.g., frequency conversion) andamplification, and outputs a modulated signal 8302_1. Thereafter, themodulated signal 8302_1 is output from an antenna 8303_1 as a radiowave.

Similarly, the modulated signals z2 (5203_1 to 5203_M) are input to awireless processing unit 8301_2. The wireless processing unit 8301_2performs signal processing (e.g., frequency conversion) andamplification, and outputs a modulated signal 8302_2. Thereafter, themodulated signal 8302_2 is output from an antenna 8303_2 as a radiowave.

As set forth above, it is permissible to use the transmission schemedescribed in Embodiment A1 while performing frequency conversion andamplification simultaneously on modulated signals having differentfrequency bandwidths.

Embodiment B1

The following describes a structural example of an application of thetransmission schemes and reception schemes shown in the aboveembodiments and a system using the application.

FIG. 84 shows an example of the structure of a system that includesdevices implementing the transmission schemes and reception schemesdescribed in the above embodiments. The transmission scheme andreception scheme described in the above embodiments are implemented in adigital broadcasting system 8400, as shown in FIG. 84, that includes abroadcasting station and a variety of reception devices such as atelevision 8411, a DVD recorder 8412, a Set Top Box (STB) 8413, acomputer 8420, an in-car television 8441, and a mobile phone 8430.Specifically, the broadcasting station 8401 transmits multiplexed data,in which video data, audio data, and the like are multiplexed, using thetransmission schemes in the above embodiments over a predeterminedbroadcasting band.

An antenna (for example, antennas 8560 and 8440) internal to eachreception device, or provided externally and connected to the receptiondevice, receives the signal transmitted from the broadcasting station8401. Each reception device obtains the multiplexed data by using thereception schemes in the above embodiments to demodulate the signalreceived by the antenna. In this way, the digital broadcasting system8400 obtains the advantageous effects of the present invention describedin the above embodiments.

The video data included in the multiplexed data has been coded with amoving picture coding method compliant with a standard such as MovingPicture Experts Group (MPEG)-2, MPEG-4 Advanced Video Coding (AVC),VC-1, or the like. The audio data included in the multiplexed data hasbeen encoded with an audio coding method compliant with a standard suchas Dolby Audio Coding (AC)-3, Dolby Digital Plus, Meridian LosslessPacking (MLP), Digital Theater Systems (DTS), DTS-HD, Linear Pulse-CodeModulation (PCM), or the like.

FIG. 85 is a schematic view illustrating an exemplary structure of areception device 8500 for carrying out the reception schemes describedin the above embodiments. As illustrated in FIG. 85, in one exemplarystructure, the reception device 8500 may be composed of a modem portionimplemented on a single LSI (or a single chip set) and a codec portionimplemented on another single LSI (or another single chip set). Thereception device 8500 shown in FIG. 85 corresponds to a component thatis included, for example, in the television 8411, the DVD recorder 8412,the STB 8413, the computer 8420, the in-car television 8441, the mobilephone 8430, or the like illustrated in FIG. 84. The reception device8500 includes a tuner 8501, for transforming a high-frequency signalreceived by an antenna 8560 into a baseband signal, and a demodulationunit 8502, for demodulating multiplexed data from the baseband signalobtained by frequency conversion. The reception schemes described in theabove embodiments are implemented in the demodulation unit 8502, thusobtaining the advantageous effects of the present invention described inthe above embodiments.

The reception device 8500 includes a stream input/output unit 8520, asignal processing unit 8504, an audio output unit 8506, and a videodisplay unit 8507. The stream input/output unit 8520 demultiplexes videoand audio data from multiplexed data obtained by the demodulation unit8502. The signal processing unit 8504 decodes the demultiplexed videodata into a video signal using an appropriate method picture decodingmethod and decodes the demultiplexed audio data into an audio signalusing an appropriate audio decoding scheme. The audio output unit 8506,such as a speaker, produces audio output according to the decoded audiosignal. The video display unit 8507, such as a display monitor, producesvideo output according to the decoded video signal.

For example, the user may operate the remote control 8550 to select achannel (of a TV program or audio broadcast), so that informationindicative of the selected channel is transmitted to an operation inputunit 8510. In response, the reception device 8500 demodulates, fromamong signals received with the antenna 8560, a signal carried on theselected channel and applies error correction decoding, so thatreception data is extracted. At this time, the reception device 8500receives control symbols included in a signal corresponding to theselected channel and containing information indicating the transmissionscheme (the transmission scheme, modulation scheme, error correctionscheme, and the like in the above embodiments) of the signal (exactly asdescribed in Embodiments A1 through A4 and as shown in FIGS. 5 and 41).With this information, the reception device 8500 is enabled to makeappropriate settings for the receiving operations, demodulation scheme,scheme of error correction decoding, and the like to duly receive dataincluded in data symbols transmitted from a broadcasting station (basestation). Although the above description is directed to an example inwhich the user selects a channel using the remote control 8550, the samedescription applies to an example in which the user selects a channelusing a selection key provided on the reception device 8500.

With the above structure, the user can view a broadcast program that thereception device 8500 receives by the reception schemes described in theabove embodiments.

The reception device 8500 according to this embodiment may additionallyinclude a recording unit (drive) 8508 for recording various data onto arecording medium, such as a magnetic disk, optical disc, or anon-volatile semiconductor memory. Examples of data to be recorded bythe recording unit 8508 include data contained in multiplexed data thatis obtained as a result of demodulation and error correction decoding bythe demodulation unit 8502, data equivalent to such data (for example,data obtained by compressing the data), and data obtained by processingthe moving pictures and/or audio. (Note here that there may be a casewhere no error correction decoding is applied to a signal obtained as aresult of demodulation by the demodulation unit 8502 and where thereception device 8500 conducts further signal processing after errorcorrection decoding. The same holds in the following description wheresimilar wording appears.) Note that the term “optical disc” used hereinrefers to a recording medium, such as Digital Versatile Disc (DVD) or BD(Blu-ray Disc), that is readable and writable with the use of a laserbeam. Further, the term “magnetic disk” used herein refers to arecording medium, such as a floppy disk (FD, registered trademark) orhard disk, that is writable by magnetizing a magnetic substance withmagnetic flux. Still further, the term “non-volatile semiconductormemory” refers to a recording medium, such as flash memory orferroelectric random access memory, composed of semiconductorelement(s). Specific examples of non-volatile semiconductor memoryinclude an SD card using flash memory and a flash Solid State Drive(SSD). It should be naturally appreciated that the specific types ofrecording media mentioned herein are merely examples, and any othertypes of recording mediums may be usable.

With the above structure, the user can record a broadcast program thatthe reception device 8500 receives with any of the reception schemesdescribed in the above embodiments, and time-shift viewing of therecorded broadcast program is possible anytime after the broadcast.

In the above description of the reception device 8500, the recordingunit 8508 records multiplexed data obtained as a result of demodulationand error correction decoding by the demodulation unit 8502. However,the recording unit 8508 may record part of data extracted from the datacontained in the multiplexed data. For example, the multiplexed dataobtained as a result of demodulation and error correction decoding bythe demodulation unit 8502 may contain contents of data broadcastservice, in addition to video data and audio data. In this case, newmultiplexed data may be generated by multiplexing the video data andaudio data, without the contents of broadcast service, extracted fromthe multiplexed data demodulated by the demodulation unit 8502, and therecording unit 8508 may record the newly generated multiplexed data.Alternatively, new multiplexed data may be generated by multiplexingeither of the video data and audio data contained in the multiplexeddata obtained as a result of demodulation and error correction decodingby the demodulation unit 8502, and the recording unit 8508 may recordthe newly generated multiplexed data. The recording unit 8508 may alsorecord the contents of data broadcast service included, as describedabove, in the multiplexed data.

The reception device 8500 described in this embodiment may be includedin a television, a recorder (such as DVD recorder, Blu-ray recorder, HDDrecorder, SD card recorder, or the like), or a mobile telephone. In sucha case, the multiplexed data obtained as a result of demodulation anderror correction decoding by the demodulation unit 8502 may contain datafor correcting errors (bugs) in software used to operate the televisionor recorder or in software used to prevent disclosure of personal orconfidential information. If such data is contained, the data isinstalled on the television or recorder to correct the software errors.Further, if data for correcting errors (bugs) in software installed inthe reception device 8500 is contained, such data is used to correcterrors that the reception device 8500 may have. This arrangement ensuresmore stable operation of the TV, recorder, or mobile phone in which thereception device 8500 is implemented.

Note that it may be the stream input/output unit 8503 that handlesextraction of data from the whole data contained in multiplexed dataobtained as a result of demodulation and error correction decoding bythe demodulation unit 8502 and multiplexing of the extracted data. Morespecifically, under instructions given from a control unit notillustrated in the figures, such as a CPU, the stream input/output unit8503 demultiplexes video data, audio data, contents of data broadcastservice etc. from the multiplexed data demodulated by the demodulationunit 8502, extracts specific pieces of data from the demultiplexed data,and multiplexes the extracted data pieces to generate new multiplexeddata. The data pieces to be extracted from demultiplexed data may bedetermined by the user or determined in advance for the respective typesof recording mediums.

With the above structure, the reception device 8500 is enabled toextract and record only data necessary to view a recorded broadcastprogram, which is effective to reduce the size of data to be recorded.

In the above description, the recording unit 8508 records multiplexeddata obtained as a result of demodulation and error correction decodingby the demodulation unit 8502. Alternatively, however, the recordingunit 8508 may record new multiplexed data generated by multiplexingvideo data newly yielded by encoding the original video data containedin the multiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8502. Here, the movingpicture coding method to be employed may be different from that used toencode the original video data, so that the data size or bit rate of thenew video data is smaller than the original video data. Here, the movingpicture coding method used to generate new video data may be of adifferent standard from that used to generate the original video data.Alternatively, the same moving picture coding method may be used butwith different parameters. Similarly, the recording unit 8508 may recordnew multiplexed data generated by multiplexing audio data newly obtainedby encoding the original audio data contained in the multiplexed dataobtained as a result of demodulation and error correction decoding bythe demodulation unit 8502. Here, the audio coding method to be employedmay be different from that used to encode the original audio data, suchthat the data size or bit rate of the new audio data is smaller than theoriginal audio data.

The process of converting the original video or audio data contained inthe multiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8502 into the video oraudio data of a different data size of bit rate is performed, forexample, by the stream input/output unit 8503 and the signal processingunit 8504. More specifically, under instructions given from the controlunit such as the CPU, the stream input/output unit 8503 demultiplexesvideo data, audio data, contents of data broadcast service etc. from themultiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8502. Under instructionsgiven from the control unit, the signal processing unit 8504 convertsthe demultiplexed video data and audio data respectively using a movingpicture coding method and an audio coding method each different from themethod that was used in the conversion applied to obtain the video andaudio data. Under instructions given from the control unit, the streaminput/output unit 8503 multiplexes the newly converted video data andaudio data to generate new multiplexed data. Note that the signalprocessing unit 8504 may perform the conversion of either or both of thevideo or audio data according to instructions given from the controlunit. In addition, the sizes of video data and audio data to be obtainedby encoding may be specified by a user or determined in advance for thetypes of recording mediums.

With the above arrangement, the reception device 8500 is enabled torecord video and audio data after converting the data to a sizerecordable on the recording medium or to a size or bit rate that matchesthe read or write rate of the recording unit 8508. This arrangementenables the recoding unit to duly record a program, even if the sizerecordable on the recording medium is smaller than the data size of themultiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8502, or if the rate atwhich the recording unit records or reads is lower than the bit rate ofthe multiplexed data. Consequently, time-shift viewing of the recordedprogram by the user is possible anytime after the broadcast.

Furthermore, the reception device 8500 additionally includes a streamoutput interface (IF) 8509 for transmitting multiplexed data demodulatedby the demodulation unit 8502 to an external device via a transportmedium 8530. In one example, the stream output IF 8509 may be a wirelesscommunication device that transmits multiplexed data via a wirelessmedium (equivalent to the transport medium 8530) to an external deviceby modulating the multiplexed data in accordance with a wirelesscommunication scheme compliant with a wireless communication standardsuch as Wi-Fi (registered trademark, a set of standards including IEEE802.11a, IEEE 802.11b, IEEE 802.11g, and IEEE 802.11n), WiGiG, WirelessHD, Bluetooth (registered trademark), ZigBee (registered trademark), orthe like. The stream output IF 8509 may also be a wired communicationdevice that transmits multiplexed data via a transmission line(equivalent to the transport medium 8530) physically connected to thestream output IF 8509 to an external device, modulating the multiplexeddata using a communication scheme compliant with wired communicationstandards, such as Ethernet (registered trademark), Universal Serial Bus(USB), Power Line Communication (PLC), or High-Definition MultimediaInterface (HDMI).

With the above structure, the user can use, on an external device,multiplexed data received by the reception device 8500 using thereception scheme described according to the above embodiments. The usageof multiplexed data by the user mentioned herein includes use of themultiplexed data for real-time viewing on an external device, recordingof the multiplexed data by a recording unit included in an externaldevice, and transmission of the multiplexed data from an external deviceto a yet another external device.

In the above description of the reception device 8500, the stream outputIF 8509 outputs multiplexed data obtained as a result of demodulationand error correction decoding by the demodulation unit 8502. However,the reception device 8500 may output data extracted from data containedin the multiplexed data, rather than the whole data contained in themultiplexed data. For example, the multiplexed data obtained as a resultof demodulation and error correction decoding by the demodulation unit8502 may contain contents of data broadcast service, in addition tovideo data and audio data. In this case, the stream output IF 8509 mayoutput multiplexed data newly generated by multiplexing video and audiodata extracted from the multiplexed data obtained as a result ofdemodulation and error correction decoding by the demodulation unit8502. In another example, the stream output IF 8509 may outputmultiplexed data newly generated by multiplexing either of the videodata and audio data contained in the multiplexed data obtained as aresult of demodulation and error correction decoding by the demodulationunit 8502.

Note that it may be the stream input/output unit 8503 that handlesextraction of data from the whole data contained in multiplexed dataobtained as a result of demodulation and error correction decoding bythe demodulation unit 8502 and multiplexing of the extracted data. Morespecifically, under instructions given from a control unit notillustrated in the figures, such as a Central Processing Unit (CPU), thestream input/output unit 8503 demultiplexes video data, audio data,contents of data broadcast service etc. from the multiplexed datademodulated by the demodulation unit 8502, extracts specific pieces ofdata from the demultiplexed data, and multiplexes the extracted datapieces to generate new multiplexed data. The data pieces to be extractedfrom demultiplexed data may be determined by the user or determined inadvance for the respective types of the stream output IF 8509.

With the above structure, the reception device 8500 is enabled toextract and output only data necessary for an external device, which iseffective to reduce the communication bandwidth used to output themultiplexed data.

In the above description, the stream output IF 8509 outputs multiplexeddata obtained as a result of demodulation and error correction decodingby the demodulation unit 8502. Alternatively, however, the stream outputIF 8509 may output new multiplexed data generated by multiplexing videodata newly yielded by encoding the original video data contained in themultiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8502. The new video data isencoded with a moving picture coding method different from that used toencode the original video data, so that the data size or bit rate of thenew video data is smaller than the original video data. Here, the movingpicture coding method used to generate new video data may be of adifferent standard from that used to generate the original video data.Alternatively, the same moving picture coding method may be used butwith different parameters. Similarly, the stream output IF 8509 mayoutput new multiplexed data generated by multiplexing audio data newlyobtained by encoding the original audio data contained in themultiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8502. The new audio data isencoded with an audio coding method different from that used to encodethe original audio data, such that the data size or bit rate of the newaudio data is smaller than the original audio data.

The process of converting the original video or audio data contained inthe multiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8502 into the video oraudio data of a different data size of bit rate is performed, forexample, by the stream input/output unit 8503 and the signal processingunit 8504. More specifically, under instructions given from the controlunit, the stream input/output unit 8503 demultiplexes video data, audiodata, contents of data broadcast service etc. from the multiplexed dataobtained as a result of demodulation and error correction decoding bythe demodulation unit 8502. Under instructions given from the controlunit, the signal processing unit 8504 converts the demultiplexed videodata and audio data respectively using a moving picture coding methodand an audio coding method each different from the method that was usedin the conversion applied to obtain the video and audio data. Underinstructions given from the control unit, the stream input/output unit8503 multiplexes the newly converted video data and audio data togenerate new multiplexed data. Note that the signal processing unit 8504may perform the conversion of either or both of the video or audio dataaccording to instructions given from the control unit. In addition, thesizes of video data and audio data to be obtained by conversion may bespecified by the user or determined in advance for the types of thestream output IF 8509.

With the above structure, the reception device 8500 is enabled to outputvideo and audio data after converting the data to a bit rate thatmatches the transfer rate between the reception device 8500 and anexternal device. This arrangement ensures that even if multiplexed dataobtained as a result of demodulation and error correction decoding bythe demodulation unit 8502 is higher in bit rate than the data transferrate to an external device, the stream output IF duly outputs newmultiplexed data at an appropriate bit rate to the external device.Consequently, the user can use the new multiplexed data on anothercommunication device.

Furthermore, the reception device 8500 also includes an audio and visualoutput interface (hereinafter, AV output IF) 8511 that outputs video andaudio signals decoded by the signal processing unit 8504 to an externaldevice via an external transport medium. In one example, the AV outputIF 8511 may be a wireless communication device that transmits modulatedvideo and audio signals via a wireless medium to an external device,using a wireless communication scheme compliant with wirelesscommunication standards, such as Wi-Fi (registered trademark), which isa set of standards including IEEE 802.11a, IEEE 802.11b, IEEE 802.11g,and IEEE 802.11n, WiGiG, Wireless HD, Bluetooth (registered trademark),ZigBee (registered trademark), or the like. In another example, thestream output IF 8509 may be a wired communication device that transmitsmodulated video and audio signals via a transmission line physicallyconnected to the stream output IF 8509 to an external device, using acommunication scheme compliant with wired communication standards, suchas Ethernet (registered trademark), USB, PLC, HDMI, or the like. In yetanother example, the stream output IF 8509 may be a terminal forconnecting a cable to output the video and audio signals in analog form.

With the above structure, the user is allowed to use, on an externaldevice, the video and audio signals decoded by the signal processingunit 8504.

Furthermore, the reception device 8500 additionally includes anoperation input unit 8510 for receiving a user operation. According tocontrol signals indicative of user operations input to the operationinput unit 8510, the reception device 8500 performs various operations,such as switching the power ON or OFF, switching the reception channel,switching the display of subtitle text ON or OFF, switching the displayof subtitle text to another language, changing the volume of audiooutput of the audio output unit 8506, and changing the settings ofchannels that can be received.

Additionally, the reception device 8500 may have a function ofdisplaying the antenna level indicating the quality of the signal beingreceived by the reception device 8500. Note that the antenna level is anindicator of the reception quality calculated based on, for example, theReceived Signal Strength Indication, Received Signal Strength Indicator(RSSI), received field strength, Carrier-to-noise power ratio (C/N), BitError Rate (BER), packet error rate, frame error rate, and channel stateinformation of the signal received on the reception device 8500. Inother words, the antenna level is a signal indicating the level andquality of the received signal. In this case, the demodulation unit 8502also includes a reception quality measuring unit for measuring thereceived signal characteristics, such as RSSI, received field strength,C/N, BER, packet error rate, frame error rate, and channel stateinformation. In response to a user operation, the reception device 8500displays the antenna level (i.e., signal indicating the level andquality of the received signal) on the video display unit 8507 in amanner identifiable by the user. The antenna level (i.e., signalindicating the level and quality of the received signal) may benumerically displayed using a number that represents RSSI, receivedfield strength, C/N, BER, packet error rate, frame error rate, channelstate information or the like. Alternatively, the antenna level may bedisplayed using an image representing RSSI, received field strength,C/N, BER, packet error rate, frame error rate, channel state informationor the like. Furthermore, the reception device 8500 may display aplurality of antenna levels (signals indicating the level and quality ofthe received signal) calculated for each of the plurality of streams s1,s2, . . . received and separated using the reception schemes shown inthe above embodiments, or one antenna level (signal indicating the leveland quality of the received signal) calculated from the plurality ofstreams s1, s2, . . . . When video data and audio data composing aprogram are transmitted hierarchically, the reception device 8500 mayalso display the signal level (signal indicating the level and qualityof the received signal) for each hierarchical level.

With the above structure, users are able to grasp the antenna level(signal indicating the level and quality of the received signal)numerically or visually during reception with the reception schemesshown in the above embodiments.

Although the reception device 8500 is described above as having theaudio output unit 8506, video display unit 8507, recording unit 8508,stream output IF 8509, and AV output IF 8511, it is not necessary forthe reception device 8500 to have all of these units. As long as thereception device 8500 is provided with at least one of the unitsdescribed above, the user is enabled to use multiplexed data obtained asa result of demodulation and error correction decoding by thedemodulation unit 8502. The reception device 8300 may therefore includeany combination of the above-described units depending on its intendeduse.

(Multiplexed Data)

The following is a detailed description of an exemplary structure ofmultiplexed data. The data structure typically used in broadcasting isan MPEG2 transport stream (TS), so therefore the following descriptionis given by way of an example related to MPEG2-TS. It should benaturally appreciated, however, that the data structure of multiplexeddata transmitted by the transmission and reception schemes described inthe above embodiments is not limited to MPEG2-TS and the advantageouseffects of the above embodiments are achieved even if any other datastructure is employed.

FIG. 86 is a view illustrating an exemplary multiplexed data structure.As illustrated in FIG. 86, multiplexed data is obtained by multiplexingone or more elementary streams, which are elements constituting abroadcast program (program or an event which is part of a program)currently provided through respective services. Examples of elementarystreams include a video stream, audio stream, presentation graphics (PG)stream, and interactive graphics (IG) stream. In the case where abroadcast program carried by multiplexed data is a movie, the videostreams represent main video and sub video of the movie, the audiostreams represent main audio of the movie and sub audio to be mixed withthe main audio, and the PG stream represents subtitles of the movie. Theterm “main video” used herein refers to video images normally presentedon a screen, whereas “sub video” refers to video images (for example,images of text explaining the outline of the movie) to be presented in asmall window inserted within the video images. The IG stream representsan interactive display constituted by presenting GUI components on ascreen.

Each stream contained in multiplexed data is identified by an identifiercalled PID uniquely assigned to the stream. For example, the videostream carrying main video images of a movie is assigned with “0x1011”,each audio stream is assigned with a different one of “0x1100” to“0x11F”, each PG stream is assigned with a different one of “0x1200” to“0x121F”, each IG stream is assigned with a different one of “0x1400” to“0x141F”, each video stream carrying sub video images of the movie isassigned with a different one of “0x1B00” to “0x1B1F”, each audio streamof sub-audio to be mixed with the main audio is assigned with adifferent one of “0x1A00” to “0x1A1F”.

FIG. 87 is a schematic view illustrating an example of how therespective streams are multiplexed into multiplexed data. First, a videostream 8701 composed of a plurality of video frames is converted into aPES packet sequence 8702 and then into a TS packet sequence 8703,whereas an audio stream 8704 composed of a plurality of audio frames isconverted into a PES packet sequence 8705 and then into a TS packetsequence 8706. Similarly, the PG stream 8711 is first converted into aPES packet sequence 8712 and then into a TS packet sequence 8713,whereas the IG stream 8714 is converted into a PES packet sequence 8715and then into a TS packet sequence 8716. The multiplexed data 8717 isobtained by multiplexing the TS packet sequences (8703, 8706, 8713 and8716) into one stream.

FIG. 88 illustrates the details of how a video stream is divided into asequence of PES packets. In FIG. 88, the first tier shows a sequence ofvideo frames included in a video stream. The second tier shows asequence of PES packets. As indicated by arrows yy1, yy2, yy3, and yy4shown in FIG. 88, a plurality of video presentation units, namely Ipictures, B pictures, and P pictures, of a video stream are separatelystored into the payloads of PES packets on a picture-by-picture basis.Each PES packet has a PES header and the PES header stores aPresentation Time-Stamp (PTS) and Decoding Time-Stamp (DTS) indicatingthe display time and decoding time of a corresponding picture.

FIG. 89 illustrates the format of a TS packet to be eventually writtenas multiplexed data. The TS packet is a fixed length packet of 188 bytesand has a 4-byte TS header containing such information as PIDidentifying the stream and a 184-byte TS payload carrying actual data.The PES packets described above are divided to be stored into the TSpayloads of TS packets. In the case of BD-ROM, each TS packet isattached with a TP_Extra_Header of 4 bytes to build a 192-byte sourcepacket, which is to be written as multiplexed data. The TP_Extra_Headercontains such information as an Arrival_Time_Stamp (ATS). The ATSindicates a time for starring transfer of the TS packet to the PIDfilter of a decoder. As shown on the lowest tier in FIG. 89, multiplexeddata includes a sequence of source packets each bearing a source packetnumber (SPN), which is a number incrementing sequentially from the startof the multiplexed data.

In addition to the TS packets storing streams such as video, audio, andPG streams, multiplexed data also includes TS packets storing a ProgramAssociation Table (PAT), a Program Map Table (PMT), and a Program ClockReference (PCR). The PAT in multiplexed data indicates the PID of a PMTused in the multiplexed data, and the PID of the PAT is “0”. The PMTincludes PIDs identifying the respective streams, such as video, audioand subtitles, contained in multiplexed data and attribute information(frame rate, aspect ratio, and the like) of the streams identified bythe respective PIDs. In addition, the PMT includes various types ofdescriptors relating to the multiplexed data. One of such descriptorsmay be copy control information indicating whether or not copying of themultiplexed data is permitted. The PCR includes information forsynchronizing the Arrival Time Clock (ATC), which is the time axis ofATS, with the System Time Clock (STC), which is the time axis of PTS andDTS. More specifically, the PCR packet includes information indicatingan STC time corresponding to the ATS at which the PCR packet is to betransferred.

FIG. 90 is a view illustrating the data structure of the PMT in detail.The PMT starts with a PMT header indicating, for example, the length ofdata contained in the PMT. Following the PMT header, descriptorsrelating to the multiplexed data are disposed. One example of adescriptor included in the PMT is copy control information describedabove. Following the descriptors, pieces of stream information relatingto the respective streams included in the multiplexed data are arranged.Each piece of stream information is composed of stream descriptorsindicating a stream type identifying a compression codec employed for acorresponding stream, a PID of the stream, and attribute information(frame rate, aspect ratio, and the like) of the stream. The PMT includesas many stream descriptors as the number of streams included in themultiplexed data.

When recorded onto a recoding medium, for example, the multiplexed datais recorded along with a multiplexed data information file.

FIG. 91 is a view illustrating the structure of the multiplexed datafile information. As illustrated in FIG. 91, the multiplexed datainformation file is management information of corresponding multiplexeddata and is composed of multiplexed data information, stream attributeinformation, and an entry map. Note that multiplexed data informationfiles and multiplexed data are in a one-to-one relationship.

As illustrated in FIG. 91, the multiplexed data information is composedof a system rate, playback start time, and playback end time. The systemrate indicates the maximum transfer rate of the multiplexed data to thePID filter of a system target decoder, which is described later. Themultiplexed data includes ATSs at intervals set so as not to exceed thesystem rate. The playback start time is set to the time specified by thePTS of the first video frame in the multiplexed data, whereas theplayback end time is set to the time calculated by adding the playbackperiod of one frame to the PTS of the last video frame in themultiplexed data.

FIG. 92 illustrates the structure of stream attribute informationcontained in multiplexed data file information. As illustrated in FIG.92, the stream attribute information includes pieces of attributeinformation of the respective streams included in multiplexed data, andeach piece of attribute information is registered with a correspondingPID. That is, different pieces of attribute information are provided fordifferent streams, namely a video stream, an audio stream, a PG streamand an IG stream. The video stream attribute information indicates thecompression codec employed to compress the video stream, the resolutionsof individual pictures constituting the video stream, the aspect ratio,the frame rate, and so on. The audio stream attribute informationindicates the compression codec employed to compress the audio stream,the number of channels included in the audio stream, the language of theaudio stream, the sampling frequency, and so on. These pieces ofinformation are used to initialize a decoder before playback by aplayer.

In the present embodiment, from among the pieces of information includedin the multiplexed data, the stream type included in the PMT is used. Inthe case where the multiplexed data is recorded on a recording medium,the video stream attribute information included in the multiplexed datainformation is used. More specifically, the moving picture coding methodand device described in any of the above embodiments may be modified toadditionally include a step or unit of setting a specific piece ofinformation in the stream type included in the PMT or in the videostream attribute information. The specific piece of information is forindicating that the video data is generated by the moving picture codingmethod and device described in the embodiment. With the above structure,video data generated by the moving picture coding method and devicedescribed in any of the above embodiments is distinguishable from videodata compliant with other standards.

FIG. 93 illustrates an exemplary structure of a video and audio outputdevice 9300 that includes a reception device 9304 for receiving amodulated signal carrying video and audio data or data for databroadcasting from a broadcasting station (base station). Note that thestructure of the reception device 9304 corresponds to the receptiondevice 8500 illustrated in FIG. 85. The video and audio output device9300 is installed with an Operating System (OS), for example, and alsowith a communication device 9306 (a communication device for a wirelessLocal Area Network (LAN) or Ethernet, for example) for establishing anInternet connection. With this structure, hypertext (World Wide Web(WWW)) 9303 provided over the Internet can be displayed on a displayarea 9301 simultaneously with images 9302 reproduced on the display area9301 from the video and audio data or data provided by databroadcasting. By operating a remote control (which may be a mobile phoneor keyboard) 9307, the user can make a selection on the images 9302reproduced from data provided by data broadcasting or the hypertext 9303provided over the Internet to change the operation of the video andaudio output device 9300. For example, by operating the remote controlto make a selection on the hypertext 9303 provided over the Internet,the user can change the WWW site currently displayed to another site.Alternatively, by operating the remote control 9307 to make a selectionon the images 9302 reproduced from the video or audio data or dataprovided by the data broadcasting, the user can transmit informationindicating a selected channel (such as a selected broadcast program oraudio broadcasting). In response, an interface (IF) 9305 acquiresinformation transmitted from the remote control, so that the receptiondevice 9304 operates to obtain reception data by demodulation and errorcorrection decoding of a signal carried on the selected channel. At thistime, the reception device 9304 receives control symbols included in asignal corresponding to the selected channel and containing informationindicating the transmission scheme of the signal (exactly as describedin Embodiments A1 through A4 and as shown in FIGS. 5 and 41). With thisinformation, the reception device 9304 is enabled to make appropriatesettings for the receiving operations, demodulation scheme, scheme oferror correction decoding, and the like to duly receive data included indata symbols transmitted from a broadcasting station (base station).Although the above description is directed to an example in which theuser selects a channel using the remote control 9307, the samedescription applies to an example in which the user selects a channelusing a selection key provided on the video and audio output device9300.

In addition, the video and audio output device 9300 may be operated viathe Internet. For example, a terminal connected to the Internet may beused to make settings on the video and audio output device 9300 forpre-programmed recording (storing). (The video and audio output device9300 therefore would have the recording unit 8508 as illustrated in FIG.85.) In this case, before starting the pre-programmed recording, thevideo and audio output device 9300 selects the channel, so that thereception device 9304 operates to obtain reception data by demodulationand error correction decoding of a signal carried on the selectedchannel. At this time, the reception device 9304 receives controlsymbols included in a signal corresponding to the selected channel andcontaining information indicating the transmission scheme (thetransmission scheme, modulation scheme, error correction scheme, and thelike in the above embodiments) of the signal (exactly as described inEmbodiments A1 through A4 and as shown in FIGS. 5 and 41). With thisinformation, the reception device 9304 is enabled to make appropriatesettings for the receiving operations, demodulation scheme, scheme oferror correction decoding, and the like to duly receive data included indata symbols transmitted from a broadcasting station (base station).

Embodiment C1

Embodiment 2 describes a precoding scheme of regularly hopping betweenprecoding matrices, and (Example #1) and (Example #2) as schemes ofsetting precoding matrices in consideration of poor reception points.The present embodiment is directed to generalization of (Example #1) and(Example #2) described in Embodiment 2.

With respect to a scheme of regularly hopping between precoding matriceswith an N-slot period (cycle), a precoding matrix prepared for an N-slotperiod (cycle) is represented as follows.

Math 566

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({\mathbb{i}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 1}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. (Let a>0.) In the presentembodiment, a unitary matrix is used and the precoding matrix inEquation #1 is represented as follows.

Math 567

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({\mathbb{i}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 2}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. (Let α>0.) (In order tosimplify the mapping performed by the transmission device and thereception device, it is preferable that λ be one of the following fixedvalues: 0 radians; π/2 radians; π radians; and (3π)/2 radians.)Embodiment 2 is specifically implemented under the assumption α=1. InEmbodiment 2, Equation #2 is represented as follows.

Math 568

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({\mathbb{i}})}} & {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 3}}\end{matrix}$

In order to distribute the poor reception points evenly with regards tophase in the complex plane, as described in Embodiment 2, Condition #101or #102 is provided in Equation #1 or #2.

Math 569

$\begin{matrix}{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {{{\mathbb{e}}^{j}\left( \frac{\pi}{N} \right)}\mspace{14mu}{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\cdots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{20mu}{\# 101}}\end{matrix}$Math 570

$\begin{matrix}{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {{{\mathbb{e}}^{j}\left( {- \frac{\pi}{N}} \right)}\mspace{14mu}{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\cdots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{20mu}{\# 102}}\end{matrix}$

Especially, when θ₁₁(i) is a fixed value independent of i, Condition#103 or #104 may be provided.

Math 571

$\begin{matrix}{\frac{{\mathbb{e}}^{{j\theta}_{11}{({x + 1})}}}{{\mathbb{e}}^{j\;{\theta\mspace{11mu}}_{21}{(x)}}} = {{{\mathbb{e}}^{j}\left( \frac{\pi}{N} \right)}\mspace{14mu}{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\cdots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{20mu}{\# 103}}\end{matrix}$Math 572

$\begin{matrix}{\frac{{\mathbb{e}}^{j\;{\theta_{21}{({x + 1})}}}}{{\mathbb{e}}^{j\;{\theta_{21}{(x)}}}} = {{{\mathbb{e}}^{j}\left( {- \frac{\pi}{N}} \right)}\mspace{14mu}{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\cdots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{20mu}{\# 104}}\end{matrix}$

Similarly, when θ₂₁(i) is a fixed value independent of i, Condition #105or #106 may be provided.

Math 573

$\begin{matrix}{\frac{{\mathbb{e}}^{{j\theta}_{11}{({x + 1})}}}{{\mathbb{e}}^{{j\theta}_{11}{(x)}}} = {{{\mathbb{e}}^{j}\left( \frac{\pi}{N} \right)}\mspace{14mu}{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\cdots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{20mu}{\# 105}}\end{matrix}$Math 574

$\begin{matrix}{\frac{{\mathbb{e}}^{j\;{\theta_{11}{({x + 1})}}}}{{\mathbb{e}}^{j\;{\theta_{11}{(x)}}}} = {{{\mathbb{e}}^{j}\left( {- \frac{\pi}{N}} \right)}\mspace{14mu}{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\cdots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{20mu}{\# 106}}\end{matrix}$

The following is an example of a precoding matrix using theabove-mentioned unitary matrix for the scheme of regularly hoppingbetween precoding matrices with an N-slot period (cycle). A precodingmatrix that is based on Equation #2 and prepared for an N-slot period(cycle) is represented as follows. (In Equation #2, λ is 0 radians, andθ₁₁(i) is 0 radians.)

Math 575

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{a^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{(i)}}}} & {\mathbb{e}}^{j{({{{\theta\;}_{21}{(i)}} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 10}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. (Let α>0.) Also, Condition#103 or #104 is satisfied. In addition, θ₂₁(i=0) may be set to a certainvalue, such as 0 radians.

With respect to a scheme of regularly hopping between precoding matriceswith an N-slot period (cycle), another example of a precoding matrixprepared for an N-slot period (cycle) is represented as follows. (InEquation #2, λ is 0 radians, and θ₁₁(i) is 0 radians.)

Math 576

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{a^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j\;\pi}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{(i)}}}} & {\mathbb{e}}^{{j\;{\theta\;}_{21}{(i)}}\;}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 9}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. (Let α>0.) Also, Condition#103 or #104 is satisfied. In addition, θ₂₁(i=0) may be set to a certainvalue, such as 0 radians.

As yet another example, a precoding matrix prepared for an N-slot period(cycle) is represented as follows. (In Equation #2, λ is 0 radians, andθ₂₁(i) is 0 radians.)

Math 577

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{a^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{(i)}}} & {\alpha \times {\mathbb{e}}^{j\;{({\theta_{11}{(i)}})}}} \\{\alpha \times {\mathbb{e}}^{j\; 0}} & {\mathbb{e}}^{j\;\pi}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 12}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. (Let α>0.) Also, Condition#105 or #106 is satisfied. In addition, θ₁₁(i=0) may be set to a certainvalue, such as 0 radians.

As yet another example, a precoding matrix prepared for an N-slot period(cycle) is represented as follows.

(In Equation #2, λ is π radians, and θ₂₁(i) is 0 radians.)

Math 578

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{a^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{(i)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \pi})}}} \\{\alpha \times {\mathbb{e}}^{j\; 0}} & {\mathbb{e}}^{j\; 0}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 13}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1 (let α>0), and Condition #105or #106 is satisfied. In addition, θ₁₁(i=0) may be set to a certainvalue, such as 0 radians.

In view of the examples of Embodiment 2, yet another example of aprecoding matrix prepared for an N-slot period (cycle) is represented asfollows. (In Equation #3, λ is 0 radians, and θ₁₁(i) is 0 radians.)

Math 579

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\;{\theta_{21}{(i)}}} & {\mathbb{e}}^{j\;{({{\theta_{21}{(i)}} + \pi}}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 14}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1, and Condition #103 or #104 issatisfied. In addition, θ₂₁(i=0) may be set to a certain value, such as0 radians.

With respect to a scheme of regularly hopping between precoding matriceswith an N-slot period (cycle), yet another example of a precoding matrixprepared for an N-slot period (cycle) is represented as follows. (InEquation #3, λ is π radians, and θ₁₁(i) is 0 radians.)

Math 580

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\;\pi} \\{\mathbb{e}}^{{j\theta}_{21}{(i)}} & {\mathbb{e}}^{j\;{\theta_{21}{(i)}}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 15}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1, and Condition #103 or #104 issatisfied. In addition, θ₂₁(i=0) may be set to a certain value, such as0 radians.

As yet another example, a precoding matrix prepared for an N-slot period(cycle) is represented as follows. (In Equation #3, λ is 0 radians, andθ₂₁(i) is 0 radians.)

Math 581

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\mathbb{e}}^{j\;{({\theta_{11}{(i)}})}} \\{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\pi}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 16}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1, and Condition #105 or #106 issatisfied. In addition, θ₁₁(i=0) may be set to a certain value, such as0 radians.

As yet another example, a precoding matrix prepared for an N-slot period(cycle) is represented as follows. (In Equation #3, λ is π radians, andθ₂₁(i) is 0 radians.)

Math 582

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{(i)}}}\;} & {\alpha \times {\mathbb{e}}^{j\;{({{\theta_{11}{(i)}} + \pi})}}} \\{\alpha \times {\mathbb{e}}^{j\; 0}} & {\mathbb{e}}^{j\; 0}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 17}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1, and Condition #105 or #106 issatisfied. In addition, θ₁₁(i=0) may be set to a certain value, such as0 radians.

As compared to the precoding scheme of regularly hopping betweenprecoding matrices described in Embodiment 9, the precoding schemepertaining to the present embodiment has a probability of achieving highdata reception quality even if the length of the period (cycle)pertaining to the present embodiment is reduced to approximately half ofthe length of the period (cycle) pertaining to Embodiment 9. Therefore,the precoding scheme pertaining to the present embodiment can reduce thenumber of precoding matrices to be prepared, which brings about theadvantageous effect of reducing the scale of circuits for thetransmission device and the reception device. The above advantageouseffect can be enhanced with a transmission device that is provided withone encoder and distributes encoded data as shown in FIG. 4, or with areception device corresponding to such a transmission device.

A preferable example of a appearing in the above examples can beobtained by using any of the schemes described in Embodiment 18.However, a is not limited to being obtained in this way.

In the present embodiment, the scheme of structuring N differentprecoding matrices for a precoding hopping scheme with an N-slot timeperiod (cycle) has been described. In this case, the N differentprecoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] areprepared. In the case of a single-carrier transmission scheme, the orderF[0], F[1], F[2], . . . , F[N−2], F[N−1] is maintained in the timedomain (or the frequency domain). The present invention is not, however,limited in this way, and the N different precoding matrices F[0], F[1],F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may beadapted to a multi-carrier transmission scheme such as an OFDMtransmission scheme or the like. As in Embodiment 1, as a scheme ofadaption in this case, precoding weights may be changed by arrangingsymbols in the frequency domain and in the frequency-time domain. Notethat a precoding hopping scheme with an N-slot period (cycle) has beendescribed, but the same advantageous effects may be obtained by randomlyusing N different precoding matrices. In other words, the N differentprecoding matrices do not necessarily need to be used in a regularperiod (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slotsN in the period (cycle) of the above scheme of regularly hopping betweenprecoding matrices), when the N different precoding matrices of thepresent embodiment are included, the probability of excellent receptionquality increases.

Embodiment C2

The following describes a precoding scheme of regularly hopping betweenprecoding matrices that is different from Embodiment C1 where Embodiment9 is incorporated—i.e., a scheme of implementing Embodiment C1 in a casewhere the number of slots in a period (cycle) is an odd number inEmbodiment 9.

With respect to a scheme of regularly hopping between precoding matriceswith an N-slot period (cycle), a precoding matrix prepared for an N-slotperiod (cycle) is represented as follows.

Math 583

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{(i)}}}\;} & {\alpha \times {\mathbb{e}}^{j\;{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\mspace{11mu}{\theta_{21}{(i)}}}} & {\mathbb{e}}^{j\;{({{\theta_{21}{(i)}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 18}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1 (let α>0). In the presentembodiment, a unitary matrix is used and the precoding matrix inEquation #1 is represented as follows.

Math 584

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{(i)}}}\;} & {\alpha \times {\mathbb{e}}^{j\;{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\mspace{11mu}{\theta_{21}{(i)}}}} & {\mathbb{e}}^{j(\;{{\theta_{21}{(i)}} + \lambda + \pi})}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 19}}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1 (let α>0). (In order tosimplify the mapping performed by the transmission device and thereception device, it is preferable that λ be one of the following fixedvalues: 0 radians; π/2 radians; π radians; and (3π)/2 radians.)Specifically, it is assumed here that α=1. Here, Equation #19 isrepresented as follows.

Math 585

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{(i)}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{11}{(i)}} + \lambda})}} \\{\mathbb{e}}^{j\mspace{11mu}{\theta_{21}{(i)}}} & {\mathbb{e}}^{j\;{({{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 20}}\end{matrix}$

The precoding matrices used in the precoding scheme of regularly hoppingbetween precoding matrices pertaining to the present embodiment areexpressed in the above manner. The present embodiment is characterizedin that the number of slots in an N-slot period (cycle) for theprecoding scheme of regularly hopping between precoding matricespertaining to the present embodiment is an odd number, i.e., expressedas N=2n+1. To realize an N-slot period (cycle) where N=2n+1, the numberof different precoding matrices to be prepared is n+1 (note, thedescription of these different precoding matrices will be given later).From among the n+1 different precoding matrices, each of the n precodingmatrices is used twice in one period (cycle), and the remaining oneprecoding matrix is used once in one period (cycle), which results in anN-slot period (cycle) where N=2n+1. The following is a detaileddescription of these precoding matrices.

Assume that the n+1 different precoding matrices, which are necessary toimplement the precoding scheme of regularly hopping between precodingmatrices with an N-slot period (cycle) where N=2n+1, are F[0], F[1], . .. , F[i], . . . , F[n−1], F[n] (i=0, 1, 2, . . . , n−2, n−1, n). Here,the n+1 different precoding matrices F[0], F[1], . . . , F[i], . . . ,F[n−1], F[n] based on Equation #19 are represented as follows.

Math 586

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;\theta_{11}} & {\alpha \times {\mathbb{e}}^{j\;{({\theta_{11} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{({{\theta\; 11} + \frac{2\; i\;\pi}{{2\; n} + 1}})}}} & {\mathbb{e}}^{j\;{({\theta_{11} + \frac{2\; i\;\pi}{{2n} + 1} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 21}}\end{matrix}$

In this case, i=0, 1, 2, . . . , n−2, n−1, n. Out of the n+1 differentprecoding matrices according to Equation #21 (namely, F[0], F[1], . . ., F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1]through F[n] is used twice (i.e., F[1] is used twice, F[2] is usedtwice, . . . , F[n−1] is used twice, and F[n] is used twice). As aresult, the precoding scheme of regularly hopping between precodingmatrices with an N-slot period (cycle) where N=2n+1 is achieved, and thereception device can achieve excellent data reception quality, similarlyto the case where the number of slots in a period (cycle) for theprecoding scheme of regularly hopping between precoding matrices is anodd number in Embodiment 9. In this case, high data reception qualitymay be achieved even if the length of the period (cycle) pertaining tothe present embodiment is reduced to approximately half of the length ofthe period (cycle) pertaining to Embodiment 9. This can reduce thenumber of precoding matrices to be prepared, which brings about theadvantageous effect of reducing the scale of circuits for thetransmission device and the reception device.

The above advantageous effect can be enhanced with a transmission devicethat is provided with one encoder and distributes encoded data as shownin FIG. 4, or with a reception device corresponding to such atransmission device.

Especially, when λ=0 radians and θ₁₁=0 radians, the above equation canbe expressed as follows.

Math 587

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;{(\frac{2\; i\;\pi}{{2\; n} + 1})}}} & {\mathbb{e}}^{j\;{({\frac{2i\;\pi}{{2\; n} + 1} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 22}}\end{matrix}$

In this case, i=0, 1, 2, . . . , n−2, n−1, n. Out of the n+1 differentprecoding matrices according to Equation #22 (namely, F[0], F[1], . . ., F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1]through F[n] is used twice (i.e., F[1] is used twice, F[2] is usedtwice, . . . , F[n−1] is used twice, and F[n] is used twice). As aresult, the precoding scheme of regularly hopping between precodingmatrices with an N-slot period (cycle) where N=2n+1 is achieved, and thereception device can achieve excellent data reception quality, similarlyto the case where the number of slots in a period (cycle) for theprecoding scheme of regularly hopping between precoding matrices is anodd number in Embodiment 9. In this case, high data reception qualitymay be achieved even if the length of the period (cycle) pertaining tothe present embodiment is reduced to approximately half of the length ofthe period (cycle) pertaining to Embodiment 9. This can reduce thenumber of precoding matrices to be prepared, which brings about theadvantageous effect of reducing the scale of circuits for thetransmission device and the reception device.

Especially, when λ=π radians and θ₁₁=0 radians, the following equationis true.

Math 588

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\; 0}\;} & {\alpha \times {\mathbb{e}}^{j\;\pi}} \\{\alpha \times {\mathbb{e}}^{j\;{(\frac{2\; i\;\pi}{{2\; n} + 1})}}} & {\mathbb{e}}^{j\;{(\frac{2\; i\;\pi}{{2\; n} + 1})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 23}}\end{matrix}$

In this case, i=0, 1, 2, . . . , n−2, n−1, n. Out of the n+1 differentprecoding matrices according to Equation #23 (namely, F[0], F[1], . . ., F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1]through F[n] is used twice (i.e., F[1] is used twice, F[2] is usedtwice, . . . , F[n−1] is used twice, and F[n] is used twice). As aresult, the precoding scheme of regularly hopping between precodingmatrices with an N-slot period (cycle) where N=2n+1 is achieved, and thereception device can achieve excellent data reception quality, similarlyto the case where the number of slots in a period (cycle) for theprecoding scheme of regularly hopping between precoding matrices is anodd number in Embodiment 9. In this case, high data reception qualitymay be achieved even if the length of the period (cycle) pertaining tothe present embodiment is reduced to approximately half of the length ofthe period (cycle) pertaining to Embodiment 9. This can reduce thenumber of precoding matrices to be prepared, which brings about theadvantageous effect of reducing the scale of circuits for thetransmission device and the reception device.

Furthermore, when α=1 as in the relationships shown in Equation #19 andEquation #20, Equation #21 can be expressed as follows.

Math 589

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;\theta_{11}} & {\mathbb{e}}^{j\;{({\theta_{11} + \lambda})}} \\{\mathbb{e}}^{j\;{({\theta_{11} + \frac{2\; i\;\pi}{{2\; n} + 1}})}} & {\mathbb{e}}^{j\;{({\theta_{11} + \frac{2\; i\;\pi}{{2\; n} + 1} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 24}}\end{matrix}$

In this case, i=0, 1, 2, . . . , n−2, n−1, n. Out of the n+1 differentprecoding matrices according to Equation #24 (namely, F[0], F[1], . . ., F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1]through F[n] is used twice (i.e., F[1] is used twice, F[2] is usedtwice, . . . , F[n−1] is used twice, and F[n] is used twice). As aresult, the precoding scheme of regularly hopping between precodingmatrices with an N-slot period (cycle) where N=2n+1 is achieved, and thereception device can achieve excellent data reception quality, similarlyto the case where the number of slots in a period (cycle) for theprecoding scheme of regularly hopping between precoding matrices is anodd number in Embodiment 9. In this case, high data reception qualitymay be achieved even if the length of the period (cycle) pertaining tothe present embodiment is reduced to approximately half of the length ofthe period (cycle) pertaining to Embodiment 9. This can reduce thenumber of precoding matrices to be prepared, which brings about theadvantageous effect of reducing the scale of circuits for thetransmission device and the reception device.

Similarly, when α=1 in Equation #22, the following equation is true.

Math 590

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\;{(\frac{2\; i\;\pi}{{2\; n} + 1})}} & {\mathbb{e}}^{j\;{({\frac{2\; i\;\pi}{{2\; n} + 1} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 25}}\end{matrix}$

In this case, i=0, 1, 2, . . . , n−2, n−1, n. Out of the n+1 differentprecoding matrices according to Equation #25 (namely, F[0], F[1], . . ., F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1]through F[n] is used twice (i.e., F[1] is used twice, F[2] is usedtwice, . . . , F[n−1] is used twice, and F[n] is used twice). As aresult, the precoding scheme of regularly hopping between precodingmatrices with an N-slot period (cycle) where N=2n+1 is achieved, and thereception device can achieve excellent data reception quality, similarlyto the case where the number of slots in a period (cycle) for theprecoding scheme of regularly hopping between precoding matrices is anodd number in Embodiment 9. In this case, high data reception qualitymay be achieved even if the length of the period (cycle) pertaining tothe present embodiment is reduced to approximately half of the length ofthe period (cycle) pertaining to Embodiment 9. This can reduce thenumber of precoding matrices to be prepared, which brings about theadvantageous effect of reducing the scale of circuits for thetransmission device and the reception device.

Similarly, when α=1 in Equation #23, the following equation is true.

Math 591

$\begin{matrix}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\;\pi} \\{\mathbb{e}}^{j\;{(\frac{2\; i\;\pi}{{2\; n} + 1})}} & {\mathbb{e}}^{j\;{(\frac{2\; i\;\pi}{{2\; n} + 1})}}\end{pmatrix}}} & {{Equation}\mspace{14mu}{\# 26}}\end{matrix}$

In this case, i=0, 1, 2, . . . , n−2, n−1, n. Out of the n+1 differentprecoding matrices according to Equation #26 (namely, F[0], F[1], . . ., F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1]through F[n] is used twice (i.e., F[1] is used twice, F[2] is usedtwice, . . . , F[n−1] is used twice, and F[n] is used twice). As aresult, the precoding scheme of regularly hopping between precodingmatrices with an N-slot period (cycle) where N=2n+1 is achieved, and thereception device can achieve excellent data reception quality, similarlyto the case where the number of slots in a period (cycle) for theprecoding scheme of regularly hopping between precoding matrices is anodd number in Embodiment 9. In this case, high data reception qualitymay be achieved even if the length of the period (cycle) pertaining tothe present embodiment is reduced to approximately half of the length ofthe period (cycle) pertaining to Embodiment 9. This can reduce thenumber of precoding matrices to be prepared, which brings about theadvantageous effect of reducing the scale of circuits for thetransmission device and the reception device.

A preferable example of a appearing in the above examples can beobtained by using any of the schemes described in Embodiment 18.However, a is not limited to being obtained in this way.

According to the present embodiment, in the case of a single-carriertransmission scheme, the precoding matrices W[0], W[1], . . . , W[2n−1],W[2n](which are constituted by F[0], F[1], F[2], . . . , F[n−1], F[n])for a precoding hopping scheme with a an N-slot period (cycle) whereN=2n+1 (i.e., a precoding scheme of regularly hopping between precodingmatrices with an N-slot period (cycle) where N=2n+1) are arranged in theorder W[0], W[1], . . . , W[2n−1], W[2n] in the time domain (or thefrequency domain). The present invention is not, however, limited inthis way, and the precoding matrices W[0], W[1], . . . , W[2n−1], W[2n]may be applied to a multi-carrier transmission scheme such as an OFDMtransmission scheme or the like. As in Embodiment 1, as a scheme ofadaption in this case, precoding weights may be changed by arrangingsymbols in the frequency domain and in the frequency-time domain.Although the above has described the precoding hopping scheme with anN-slot period (cycle) where N=2n+1, the same advantageous effects may beobtained by randomly using W[0], W[1], . . . , W[2n−1], W[2n]. In otherwords, W[0], W[1], . . . , W[2n−1], W[2n] do not necessarily need to beused in a regular period (cycle).

Furthermore, in the precoding matrix hopping scheme over an H-slotperiod (cycle) (H being a natural number larger than the number of slotsN=2n+1 in the period (cycle) of the above scheme of regularly hoppingbetween precoding matrices), when the N different precoding matrices ofthe present embodiment are included, the probability of excellentreception quality increases.

Embodiment C3

The present embodiment provides detailed descriptions of a case where,as shown in Non-Patent Literature 12 through Non-Patent Literature 15, aQuasi-Cyclic Low-Density Parity-Check (QC-LDPC) code (or an LDPC (block)code other than a QC-LDPC code) and a block code (e.g., a concatenatedcode consisting of an LDPC code and a Bose-Chaudhuri-Hocquenghem (BCH)code, and a turbo code) are used, especially when the scheme ofregularly hopping between precoding matrices described in Embodiments 16through 26 and C1 is employed. This embodiment describes an example oftransmitting two streams, s1 and s2. However, for the case of codingusing block codes, when control information or the like is notnecessary, the number of bits in a coded block matches the number ofbits composing the block code (the control information or the likelisted below may, however, be included therein). For the case of codingusing block codes, when control information or the like (such as acyclic redundancy check (CRC), transmission parameters, or the like) isnecessary, the number of bits in a coded block is the sum of the numberof bits composing the block code and the number of bits in the controlinformation or the like.

FIG. 97 shows a modification of the number of symbols and of slotsnecessary for one coded block when using block coding. FIG. 97 “shows amodification of the number of symbols and of slots necessary for onecoded block when using block coding” for the case when, for example asshown in the transmission device in FIG. 4, two streams, s1 and s2, aretransmitted, and the transmission device has one encoder. (In this case,the transmission scheme may be either single carrier transmission, ormulticarrier transmission such as OFDM.)

As shown in FIG. 97, the number of bits constituting one block that hasbeen encoded via block coding is set to 6,000. In order to transmitthese 6,000 bits, 3,000 symbols are required when the modulation schemeis QPSK, 1,500 when the modulation scheme is 16QAM, and 1,000 when themodulation scheme is 64QAM.

Since the transmission device in FIG. 4 simultaneously transmits twostreams, 1,500 of the 3,000 symbols when the modulation scheme is QPSKare allocated to s1, and 1,500 to s2. Therefore, 1,500 slots (the term“slot” is used here) are required to transmit the 1,500 symbolstransmitted in s1 and the 1,500 symbols transmitted in s2.

By similar reasoning, when the modulation scheme is 16QAM, 750 slots arenecessary to transmit all of the bits constituting one coded block, andwhen the modulation scheme is 64QAM, 500 slots are necessary to transmitall of the bits constituting one block.

The following describes the relationship between the slots defined aboveand the precoding matrices in the scheme of regularly hopping betweenprecoding matrices.

Here, the number of precoding matrices prepared for the scheme ofregularly hopping between precoding matrices is set to five. In otherwords, five different precoding matrices are prepared for the weightingunit in the transmission device in FIG. 4 (the weighting unit selectsone of the plurality of precoding matrices and performs precoding foreach slot). These five different precoding matrices are represented asF[0], F[1], F[2], F[3], and F[4].

When the modulation scheme is QPSK, among the 1,500 slots describedabove for transmitting the 6,000 bits constituting one coded block, itis necessary for 300 slots to use the precoding matrix F[0], 300 slotsto use the precoding matrix F[1], 300 slots to use the precoding matrixF[2], 300 slots to use the precoding matrix F[3], and 300 slots to usethe precoding matrix F[4]. This is because if use of the precodingmatrices is biased, the reception quality of data is greatly influencedby the precoding matrix that was used a greater number of times.

When the modulation scheme is 16QAM, among the 750 slots described abovefor transmitting the 6,000 bits constituting one coded block, it isnecessary for 150 slots to use the precoding matrix F[0], 150 slots touse the precoding matrix F[1], 150 slots to use the precoding matrixF[2], 150 slots to use the precoding matrix F[3], and 150 slots to usethe precoding matrix F[4].

When the modulation scheme is 64QAM, among the 500 slots described abovefor transmitting the 6,000 bits constituting one coded block, it isnecessary for 100 slots to use the precoding matrix F[0], 100 slots touse the precoding matrix F[1], 100 slots to use the precoding matrixF[2], 100 slots to use the precoding matrix F[3], and 100 slots to usethe precoding matrix F[4].

As described above, in the scheme of regularly hopping between precodingmatrices, if there are N different precoding matrices (represented asF[0], F[1], F[2], . . . , F[N−2], and F[N−1]), when transmitting all ofthe bits constituting one coded block, Condition #107 should besatisfied, wherein K₀ is the number of slots using the precoding matrixF[0], K₁ is the number of slots using the precoding matrix F[1], K_(i)is the number of slots using the precoding matrix F[i] (i=0, 1, 2, . . ., N−1), and K_(N-1) is the number of slots using the precoding matrixF[N−1].

Condition #107

K₀=K₁= . . . =K_(i)= . . . =K_(N-1), i.e. K_(a)=K_(b) (for ∀a, ∀b, wherea, b, =0, 1, 2, . . . , N−1 (each of a and b being an integer in a rangeof 0 to N−1), and a≠b).

If the communications system supports a plurality of modulation schemes,and the modulation scheme that is used is selected from among thesupported modulation schemes, then a modulation scheme for whichCondition #107 is satisfied should be selected.

When a plurality of modulation schemes are supported, it is typical forthe number of bits that can be transmitted in one symbol to vary frommodulation scheme to modulation scheme (although it is also possible forthe number of bits to be the same), and therefore some modulationschemes may not be capable of satisfying Condition #107. In such a case,instead of Condition #107, the following condition should be satisfied.

Condition #108

The difference between K_(a) and K_(b) is 0 or 1, i.e. |K_(a)−K_(b)| is0 or 1 (for ∀a, ∀b, where a, b, =0, 1, 2, . . . , N−1 (each of a and bbeing an integer in a range of 0 to N−1), and a≠b).

FIG. 98 shows a modification of the number of symbols and of slotsnecessary for two coded blocks when using block coding. FIG. 98 “shows amodification of the number of symbols and of slots necessary for twocoded blocks when using block coding” for the case when, for example asshown in the transmission device in FIG. 3 and in FIG. 13, two streamsare transmitted, i.e. s1 and s2, and the transmission device has twoencoders. (In this case, the transmission scheme may be either singlecarrier transmission, or multicarrier transmission such as OFDM.)

As shown in FIG. 98, the number of bits constituting one block that hasbeen encoded via block coding is set to 6,000. In order to transmitthese 6,000 bits, 3,000 symbols are required when the modulation schemeis QPSK, 1,500 when the modulation scheme is 16QAM, and 1,000 when themodulation scheme is 64QAM.

The transmission device in FIG. 3 or in FIG. 13 transmits two streamssimultaneously, and since two encoders are provided, different codedblocks are transmitted in the two streams. Accordingly, when themodulation scheme is QPSK, two coded blocks are transmitted in s1 and s2within the same interval. For example, a first coded block istransmitted in s1 and a second coded block is transmitted in s2, andtherefore, 3,000 slots are required to transmit the first and secondcoded blocks.

By similar reasoning, when the modulation scheme is 16QAM, 1,500 slotsare necessary to transmit all of the bits constituting two coded blocks,and when the modulation scheme is 64QAM, 1,000 slots are necessary totransmit all of the bits constituting two blocks.

The following describes the relationship between the slots defined aboveand the precoding matrices in the scheme of regularly hopping betweenprecoding matrices.

Here, the number of precoding matrices prepared for the scheme ofregularly hopping between precoding matrices is set to five. In otherwords, five different precoding matrices are prepared for the weightingunit in the transmission device in FIG. 3 or in FIG. 13 (the weightingunit selects one of the plurality of precoding matrices and performsprecoding for each slot). These five different precoding matrices arerepresented as F[0], F[1], F[2], F[3], and F[4].

When the modulation scheme is QPSK, among the 3,000 slots describedabove for transmitting the 6,000×2 bits constituting two coded blocks,it is necessary for 600 slots to use the precoding matrix F[0], 600slots to use the precoding matrix F[1], 600 slots to use the precodingmatrix F[2], 600 slots to use the precoding matrix F[3], and 600 slotsto use the precoding matrix F[4]. This is because if use of theprecoding matrices is biased, the reception quality of data is greatlyinfluenced by the precoding matrix that was used a greater number oftimes.

To transmit the first coded block, it is necessary for the slot usingthe precoding matrix F[0] to occur 600 times, the slot using theprecoding matrix F[1] to occur 600 times, the slot using the precodingmatrix F[2] to occur 600 times, the slot using the precoding matrix F[3]to occur 600 times, and the slot using the precoding matrix F[4] tooccur 600 times. To transmit the second coded block, the slot using theprecoding matrix F[0] should occur 600 times, the slot using theprecoding matrix F[1] should occur 600 times, the slot using theprecoding matrix F[2] should occur 600 times, the slot using theprecoding matrix F[3] should occur 600 times, and the slot using theprecoding matrix F[4] should occur 600 times.

Similarly, when the modulation scheme is 16QAM, among the 1,500 slotsdescribed above for transmitting the 6,000×2 bits constituting two codedblocks, it is necessary for 300 slots to use the precoding matrix F[0],300 slots to use the precoding matrix F[1], 300 slots to use theprecoding matrix F[2], 300 slots to use the precoding matrix F[3], and300 slots to use the precoding matrix F[4].

To transmit the first coded block, it is necessary for the slot usingthe precoding matrix F[0] to occur 300 times, the slot using theprecoding matrix F[1] to occur 300 times, the slot using the precodingmatrix F[2] to occur 300 times, the slot using the precoding matrix F[3]to occur 300 times, and the slot using the precoding matrix F[4] tooccur 300 times. To transmit the second coded block, the slot using theprecoding matrix F[0] should occur 300 times, the slot using theprecoding matrix F[1] should occur 300 times, the slot using theprecoding matrix F[2] should occur 300 times, the slot using theprecoding matrix F[3] should occur 300 times, and the slot using theprecoding matrix F[4] should occur 300 times.

Similarly, when the modulation scheme is 64QAM, among the 1,000 slotsdescribed above for transmitting the 6,000×2 bits constituting two codedblocks, it is necessary for 200 slots to use the precoding matrix F[0],200 slots to use the precoding matrix F[1], 200 slots to use theprecoding matrix F[2], 200 slots to use the precoding matrix F[3], and200 slots to use the precoding matrix F[4].

To transmit the first coded block, it is necessary for the slot usingthe precoding matrix F[0] to occur 200 times, the slot using theprecoding matrix F[1] to occur 200 times, the slot using the precodingmatrix F[2] to occur 200 times, the slot using the precoding matrix F[3]to occur 200 times, and the slot using the precoding matrix F[4] tooccur 200 times. To transmit the second coded block, the slot using theprecoding matrix F[0] should occur 200 times, the slot using theprecoding matrix F[1] should occur 200 times, the slot using theprecoding matrix F[2] should occur 200 times, the slot using theprecoding matrix F[3] should occur 200 times, and the slot using theprecoding matrix F[4] should occur 200 times.

As described above, in the scheme of regularly hopping between precodingmatrices, if there are N different precoding matrices (represented asF[0], F[1], F[2], . . . , F[N−2], and F[N−1]), when transmitting all ofthe bits constituting two coded blocks, Condition #109 should besatisfied, wherein K₀ is the number of slots using the precoding matrixF[0], K₁ is the number of slots using the precoding matrix F[1], K_(i)is the number of slots using the precoding matrix F[i] (i=0, 1, 2, . . ., N−1), and K_(N-1) is the number of slots using the precoding matrixF[N−1].

Condition #109

K₀=K₁= . . . =K_(i)= . . . =K_(N-1), i.e. K_(a)=K_(b) (for ∀a, ∀b, wherea, b, =0, 1, 2, . . . , N−1 (each of a and b being an integer in a rangeof 0 to N−1), and a b).

When transmitting all of the bits constituting the first coded block,Condition #110 should be satisfied, wherein K_(0,1) is the number oftimes the precoding matrix F[0] is used, K_(1,1) is the number of timesthe precoding matrix F[1] is used, K_(i,1) is the number of times theprecoding matrix F[i] is used (i=0, 1, 2, . . . , N−1), and K_(N-1,1) isthe number of times the precoding matrix F[N−1] is used.

Condition #110

K_(0,1)=K_(1,1)= . . . =K_(i,1)= . . . =K_(N-1,1), i.e. K_(a,1)=K_(b,1)(for ∀a, ∀b, where a, b,=0, 1, 2, . . . , N−1 (each of a and b being aninteger in a range of 0 to N−1), and a≠b).

When transmitting all of the bits constituting the second coded block,Condition #111 should be satisfied, wherein K_(0,2) is the number oftimes the precoding matrix F[0] is used, K_(1,2) is the number of timesthe precoding matrix F[1] is used, K_(i,2) is the number of times theprecoding matrix F[i] is used (i=0, 1, 2, . . . , N−1), and K_(N-1,2) isthe number of times the precoding matrix F[N−1] is used.

Condition #111

K_(0,2)=K_(1,2)= . . . =K_(i,2)= . . . =K_(N-1,2), i.e. K_(a,2)=K_(b,2)(for ∀a, ∀b, where a, b,=0, 1, 2, . . . , N−1(each of a and b being aninteger in a range of 0 to N−1), and a≠b).

If the communications system supports a plurality of modulation schemes,and the modulation scheme that is used is selected from among thesupported modulation schemes, the selected modulation scheme preferablysatisfies Conditions #109, #110, and #111.

When a plurality of modulation schemes are supported, it is typical forthe number of bits that can be transmitted in one symbol to vary frommodulation scheme to modulation scheme (although it is also possible forthe number of bits to be the same), and therefore some modulationschemes may not be capable of satisfying Conditions #109, #110, and#111. In such a case, instead of Conditions #109, #110, and #111, thefollowing conditions should be satisfied.

Condition #112

The difference between K_(a) and K_(b) is 0 or 1, i.e. |K_(a)−K_(b)| is0 or 1 (for ∀a, ∀b, where a, b, =0, 1, 2, . . . , N−1 (each of a and bbeing an integer in a range of 0 to N−1), and a≠b).

Condition #113 The difference between K_(a,1) and K_(b,1) is 0 or 1,i.e. |K_(a,1)−K_(b,1)| is 0 or 1 (for ∀a, ∀b, where a, b, =0, 1, 2, . .. , N−1 (each of a and b being an integer in a range of 0 to N−1), anda≠b).

Condition #114

The difference between K_(a,2) and K_(b,2) is 0 or 1, i.e.|K_(a2)−K_(b,2)| is 0 or 1 (for ∀a, ∀b, where a, b, =0, 1, 2, . . . ,N−1 (each of a and b being an integer in a range of 0 to N−1), and a≠b).

Associating coded blocks with precoding matrices in this way eliminatesbias in the precoding matrices that are used for transmitting codedblocks, thereby achieving the advantageous effect of improving receptionquality of data by the reception device.

In the present embodiment, in the scheme of regularly hopping betweenprecoding matrices, N different precoding matrices are necessary for aprecoding hopping scheme with an N-slot period (cycle). In this case,F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared as the N differentprecoding matrices. These precoding matrices may be arranged in thefrequency domain in the order of F[0], F[1], F[2], . . . , F[N−2],F[N−1], but arrangement is not limited in this way. With N differentprecoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated inthe present Embodiment, precoding weights may be changed by arrangingsymbols in the time domain or in the frequency-time domains as inEmbodiment 1. Note that a precoding hopping scheme with an N-slot period(cycle) has been described, but the same advantageous effects may beobtained by randomly using N different precoding matrices. In otherwords, the N different precoding matrices do not necessarily need to beused in a regular period (cycle). Here, when the conditions provided inthe present embodiment are satisfied, the reception device has a highpossibility of achieving excellent data reception quality.

Furthermore, as described in Embodiment 15, a spatial multiplexing MIMOsystem, a MIMO system in which precoding matrices are fixed, aspace-time block coding scheme, a one-stream-only transmission mode, andmodes for schemes of regularly hopping between precoding matrices mayexist, and the transmission device (broadcast station, base station) mayselect the transmission scheme from among these modes. In this case, inthe spatial multiplexing MIMO system, the MIMO system in which precodingmatrices are fixed, the space-time block coding scheme, theone-stream-only transmission mode, and the modes for schemes ofregularly hopping between precoding matrices, it is preferable toimplement the present embodiment in the (sub)carriers for which a schemeof regularly hopping between precoding matrices is selected.

Embodiment C4

The present embodiment provides detailed descriptions of a case where,as shown in Non-Patent Literature 12 through Non-Patent Literature 15, aQC-LDPC code (or an LDPC (block) code other than a QC-LDPC code) and ablock code (e.g., a concatenated code consisting of an LDPC code and aBCH code, and a turbo code) are used, especially when the scheme ofregularly hopping between precoding matrices described in Embodiments C2is employed. This embodiment describes an example of transmitting twostreams, s1 and s2. However, for the case of coding using block codes,when control information or the like is not necessary, the number ofbits in a coded block matches the number of bits composing the blockcode (the control information or the like listed below may, however, beincluded therein). For the case of coding using block codes, whencontrol information or the like (such as a cyclic redundancy check(CRC), transmission parameters, or the like) is necessary, the number ofbits in a coded block is the sum of the number of bits composing theblock code and the number of bits in the control information or thelike.

FIG. 97 shows a modification of the number of symbols and of slotsnecessary for one coded block when using block coding. FIG. 97 “shows amodification of the number of symbols and of slots necessary for onecoded block when using block coding” for the case when, for example asshown in the transmission device in FIG. 4, two streams, s1 and s2, aretransmitted, and the transmission device has one encoder. (In this case,the transmission scheme may be either single carrier transmission, ormulticarrier transmission such as OFDM.)

As shown in FIG. 97, the number of bits constituting one block that hasbeen encoded via block coding is set to 6,000. In order to transmitthese 6,000 bits, 3,000 symbols are required when the modulation schemeis QPSK, 1,500 when the modulation scheme is 16QAM, and 1,000 when themodulation scheme is 64QAM.

Since the transmission device in FIG. 4 simultaneously transmits twostreams, 1,500 of the 3,000 symbols when the modulation scheme is QPSKare allocated to s1, and 1,500 to s2. Therefore, 1,500 slots (the term“slot” is used here) are required to transmit the 1,500 symbolstransmitted in s1 and the 1,500 symbols transmitted in s2.

By similar reasoning, when the modulation scheme is 16QAM, 750 slots arenecessary to transmit all of the bits constituting one coded block, andwhen the modulation scheme is 64QAM, 500 slots are necessary to transmitall of the bits constituting one block.

The following describes the relationship between the slots defined aboveand the precoding matrices in the scheme of regularly hopping betweenprecoding matrices.

Here, five precoding matrices for realizing the precoding scheme ofregularly hopping between precoding matrices with a five-slot period(cycle), as described in Embodiment C2, are expressed as W[0], W[1],W[2], W[3], and W[4](the weighting unit of the transmission deviceselects one of a plurality of precoding matrices and performs precodingfor each slot).

When the modulation scheme is QPSK, among the 1,500 slots describedabove for transmitting the 6,000 bits constituting one coded block, itis necessary for 300 slots to use the precoding matrix W[0], 300 slotsto use the precoding matrix W[1], 300 slots to use the precoding matrixW[2], 300 slots to use the precoding matrix W[3], and 300 slots to usethe precoding matrix W[4]. This is because if use of the precodingmatrices is biased, the reception quality of data is greatly influencedby the precoding matrix that was used a greater number of times.

When the modulation scheme is 16QAM, among the 750 slots described abovefor transmitting the 6,000 bits constituting one coded block, it isnecessary for 150 slots to use the precoding matrix W[0], 150 slots touse the precoding matrix W[1], 150 slots to use the precoding matrixW[2], 150 slots to use the precoding matrix W[3], and 150 slots to usethe precoding matrix W[4].

When the modulation scheme is 64QAM, among the 500 slots described abovefor transmitting the 6,000 bits constituting one coded block, it isnecessary for 100 slots to use the precoding matrix W[0], 100 slots touse the precoding matrix W[1], 100 slots to use the precoding matrixW[2], 100 slots to use the precoding matrix W[3], and 100 slots to usethe precoding matrix W[4].

As described above, in the scheme of regularly hopping between precodingmatrices pertaining to Embodiment C2, provided that the precodingmatrices W[0], W[1], . . . , W[2n−1], and W[2n] (which are constitutedby F[0], F[1], F[2], . . . , F[n−1], and F[n]; see Embodiment C2) areprepared to achieve an N-slot period (cycle) where N=2n+1, whentransmitting all of the bits constituting one coded block, Condition#115 should be satisfied, wherein K₀ is the number of slots using theprecoding matrix W[0], K₁ is the number of slots using the precodingmatrix W[1], K_(i) is the number of slots using the precoding matrixW[i] (i=0, 1, 2, . . . , 2n−1, 2n), and K_(2n) is the number of slotsusing the precoding matrix W[2n].

Condition #115

K₀=K₁= . . . =K_(i)= . . . =K_(2n), i.e. K_(a)=K_(b) (for ∀a, ∀b, wherea, b, =0, 1, 2, . . . , 2n−1, 2n (each of a and b being an integer in arange of 0 to 2n), and a≠b).

In the scheme of regularly hopping between precoding matrices pertainingto Embodiment C2, provided that the different precoding matrices F[0],F[1], F[2], . . . , F[n−1], and F[n] are prepared to achieve an N-slotperiod (cycle) where N=2n+1, when transmitting all of the bitsconstituting one coded block, Condition #115 can be expressed asfollows, wherein G₀ is the number of slots using the precoding matrixF[0], G₁ is the number of slots using the precoding matrix F[1], G_(i)is the number of slots using the precoding matrix F[i] (i=0, 1, 2, . . ., n−1, n), and G_(n) is the number of slots using the precoding matrixF[n].

Condition #116

2×G₀=G₁= . . . =G_(i)= . . . =G_(n), i.e. 2×G₀=G_(a) (for ∀a, where a=1,2, . . . , n−1, n (a being an integer in a range of 1 to n)).

If the communications system supports a plurality of modulation schemes,and the modulation scheme that is used is selected from among thesupported modulation schemes, then a modulation scheme for whichCondition #115 (#116) is satisfied should be selected.

When a plurality of modulation schemes are supported, it is typical forthe number of bits that can be transmitted in one symbol to vary frommodulation scheme to modulation scheme (although it is also possible forthe number of bits to be the same), and therefore some modulationschemes may not be capable of satisfying Condition #115 (#116). In sucha case, instead of Condition #115, the following condition should besatisfied.

Condition #117

The difference between K_(a) and K_(b) is 0 or 1, i.e. |K_(a)−K_(b)| is0 or 1 (for ∀a, ∀b, where a, b, =0, 1, 2, . . . , 2n−1, 2n (each of aand b being an integer in a range of 0 to 2n), and a≠b).

Condition #117 can also be expressed as follows.

Condition #118

The difference between G_(a) and G_(b) is 0, 1 or 2, i.e. |G_(a)−G_(b)|is 0, 1 or 2 (for ∀a, ∀b, where a, b, =1, 2, . . . , n−1, n (each of aand b being an integer in a range of 1 to n), and a≠b); and

the difference between 2×G₀ and G_(a) is 0, 1 or 2, i.e. |2×G₀−G_(a)| is0, 1 or 2 (for ∀a, where a=1, 2, . . . , n−1, n (a being an integer in arange of 1 to n)).

FIG. 98 shows a modification of the number of symbols and of slotsnecessary for one coded block when using block coding. FIG. 98 “shows amodification of the number of symbols and of slots necessary for twocoded blocks when using block coding” for the case when, for example asshown in the transmission device in FIG. 3 and in FIG. 13, two streamsare transmitted, i.e. s1 and s2, and the transmission device has twoencoders. (In this case, the transmission scheme may be either singlecarrier transmission, or multicarrier transmission such as OFDM.)

As shown in FIG. 98, the number of bits constituting one block that hasbeen encoded via block coding is set to 6,000. In order to transmitthese 6,000 bits, 3,000 symbols are required when the modulation schemeis QPSK, 1,500 when the modulation scheme is 16QAM, and 1,000 when themodulation scheme is 64QAM.

The transmission device in FIG. 3 or in FIG. 13 transmits two streamssimultaneously, and since two encoders are provided, different codedblocks are transmitted in the two streams. Accordingly, when themodulation scheme is QPSK, two coded blocks are transmitted in s1 and s2within the same interval. For example, a first coded block istransmitted in s1, and a second coded block is transmitted in s2, andtherefore, 3,000 slots are required to transmit the first and secondcoded blocks.

By similar reasoning, when the modulation scheme is 16QAM, 1,500 slotsare necessary to transmit all of the bits constituting two coded blocks,and when the modulation scheme is 64QAM, 1,000 slots are necessary totransmit all of the bits constituting two blocks.

The following describes the relationship between the slots defined aboveand the precoding matrices in the scheme of regularly hopping betweenprecoding matrices.

Below, the five precoding matrices prepared in Embodiment C2 toimplement the precoding scheme of regularly hopping between precodingmatrices with a five-slot period (cycle) are expressed as W[0], W[1],W[2], W[3], and W[4]. (The weighting unit in the transmission deviceselects one of a plurality of precoding matrices and performs precodingfor each slot).

When the modulation scheme is QPSK, among the 3,000 slots describedabove for transmitting the 6,000×2 bits constituting two coded blocks,it is necessary for 600 slots to use the precoding matrix W[0], 600slots to use the precoding matrix W[1], 600 slots to use the precodingmatrix W[2], 600 slots to use the precoding matrix W[3], and 600 slotsto use the precoding matrix W[4]. This is because if use of theprecoding matrices is biased, the reception quality of data is greatlyinfluenced by the precoding matrix that was used a greater number oftimes.

To transmit the first coded block, it is necessary for the slot usingthe precoding matrix W[0] to occur 600 times, the slot using theprecoding matrix W[1] to occur 600 times, the slot using the precodingmatrix W[2] to occur 600 times, the slot using the precoding matrix W[3]to occur 600 times, and the slot using the precoding matrix W[4] tooccur 600 times. To transmit the second coded block, the slot using theprecoding matrix W[0] should occur 600 times, the slot using theprecoding matrix W[1] should occur 600 times, the slot using theprecoding matrix W[2] should occur 600 times, the slot using theprecoding matrix W[3] should occur 600 times, and the slot using theprecoding matrix W[4] should occur 600 times.

Similarly, when the modulation scheme is 16QAM, among the 1,500 slotsdescribed above for transmitting the 6,000×2 bits constituting two codedblocks, it is necessary for 300 slots to use the precoding matrix W[0],300 slots to use the precoding matrix W[1], 300 slots to use theprecoding matrix W[2], 300 slots to use the precoding matrix W[3], and300 slots to use the precoding matrix W[4].

To transmit the first coded block, it is necessary for the slot usingthe precoding matrix W[0] to occur 300 times, the slot using theprecoding matrix W[1] to occur 300 times, the slot using the precodingmatrix W[2] to occur 300 times, the slot using the precoding matrix W[3]to occur 300 times, and the slot using the precoding matrix W[4] tooccur 300 times. To transmit the second coded block, the slot using theprecoding matrix W[0] should occur 300 times, the slot using theprecoding matrix W[1] should occur 300 times, the slot using theprecoding matrix W[2] should occur 300 times, the slot using theprecoding matrix W[3] should occur 300 times, and the slot using theprecoding matrix W[4] should occur 300 times.

Similarly, when the modulation scheme is 64QAM, among the 1,000 slotsdescribed above for transmitting the 6,000×2 bits constituting two codedblocks, it is necessary for 200 slots to use the precoding matrix W[0],200 slots to use the precoding matrix W[1], 200 slots to use theprecoding matrix W[2], 200 slots to use the precoding matrix W[3], and200 slots to use the precoding matrix W[4].

To transmit the first coded block, it is necessary for the slot usingthe precoding matrix W[0] to occur 200 times, the slot using theprecoding matrix W[1] to occur 200 times, the slot using the precodingmatrix W[2] to occur 200 times, the slot using the precoding matrix W[3]to occur 200 times, and the slot using the precoding matrix W[4] tooccur 200 times. To transmit the second coded block, the slot using theprecoding matrix W[0] should occur 200 times, the slot using theprecoding matrix W[1] should occur 200 times, the slot using theprecoding matrix W[2] should occur 200 times, the slot using theprecoding matrix W[3] should occur 200 times, and the slot using theprecoding matrix W[4] should occur 200 times.

As described above, in the scheme of regularly hopping between precodingmatrices pertaining to Embodiment C2, provided that the precodingmatrices W[0], W[1], . . . , W[2n−1], and W[2n] (which are constitutedby F[0], F[1], F[2], . . . , F[n−1], and F[n]; see Embodiment C2) areprepared to achieve an N-slot period (cycle) where N=2n+1, whentransmitting all of the bits constituting two coded blocks, Condition#119 should be satisfied, wherein K₀ is the number of slots using theprecoding matrix W[0], K₁ is the number of slots using the precodingmatrix W[1], K_(i) is the number of slots using the precoding matrixW[i] (i=0, 1, 2, . . . , 2n−1, 2n), and K_(2n) is the number of slotsusing the precoding matrix W[2n].

Condition #119

K₀=K₁= . . . =K_(i)= . . . =K_(2n), i.e. K_(a)=K_(b) (for ∀a, ∀b, wherea, b, =0, 1, 2, . . . , 2n−1, 2n (each of a and b being an integer in arange of 0 to 2n), and a≠b).

When transmitting all of the bits constituting the first coded block,Condition #120 should be satisfied, wherein K_(0,1) is the number oftimes the precoding matrix W[0] is used, K_(1,1) is the number of timesthe precoding matrix W[1] is used, K_(i,1) is the number of times theprecoding matrix W[i] is used (i=0, 1, 2, . . . , 2n−1, 2n), andK_(2n,1) is the number of times the precoding matrix W[2n] is used.

Condition #120

K₀,1=K_(1,1)= . . . =K_(i,1)= . . . =K_(2n,1), i.e. K_(a,1)=K_(b,1) (for∀a, ∀b, where a, b, =0, 1, 2, . . . , 2n−1, 2n (each of a and b being aninteger in a range of 0 to 2n), and a≠b).

When transmitting all of the bits constituting the second coded block,Condition #121 should be satisfied, wherein K_(0,2) is the number oftimes the precoding matrix W[0] is used, K_(1,2) is the number of timesthe precoding matrix W[1] is used, K_(i,2) is the number of times theprecoding matrix W[i] is used (i=0, 1, 2, . . . , 2n−1, 2n), andK_(2n,2) is the number of times the precoding matrix W[2n] is used.

Condition #121

K_(0,2)=K_(1,2)= . . . =K_(i,2)= . . . =K_(2n,2), i.e. K_(a,2)=K_(b,2)(for ∀a, ∀b, where a, b, =0, 1, 2, . . . , 2n−1, 2n (each of a and bbeing an integer in a range of 0 to 2n), and a≠b).

In the scheme of regularly hopping between precoding matrices pertainingto Embodiment C2, provided that the different precoding matrices F[0],F[1], F[2], . . . , F[n−1], and F[n] are prepared to achieve an N-slotperiod (cycle) where N=2n+1, when transmitting all of the bitsconstituting two coded blocks, Condition #119 can be expressed asfollows, wherein G₀ is the number of slots using the precoding matrixF[0], G₁ is the number of slots using the precoding matrix F[1], G_(i)is the number of slots using the precoding matrix F[i] (i=0, 1, 2, . . ., n−1, n), and G_(n) is the number of slots using the precoding matrixF[n].

Condition #122

2×G₀=G₁= . . . =G_(i)= . . . =G_(n), i.e. 2×G₀=G_(a) (for ∀a, where a=1,2, . . . , n−1, n (a being an integer in a range of 1 to n)).

When transmitting all of the bits constituting the first coded block,Condition #123 should be satisfied, wherein G_(0,1) is the number oftimes the precoding matrix F[0] is used, K_(1,1) is the number of timesthe precoding matrix F[1] is used, G_(i,1) is the number of times theprecoding matrix F[i] is used (i=0, 1, 2, . . . , n−1, n), and G_(n,1)is the number of times the precoding matrix F[n] is used.

Condition #123

2×G_(0,1)=G_(1,1)= . . . =G_(i,1)= . . . =G_(n,1), i.e.2×G_(0,1)=G_(a,1) (for ∀a, where a=1, 2, . . . , n−1, n (a being aninteger in a range of 1 to n)).

When transmitting all of the bits constituting the second coded block,Condition #124 should be satisfied, wherein G_(0,2) is the number oftimes the precoding matrix F[0] is used, G_(1,2) is the number of timesthe precoding matrix F[1] is used, G_(i,2) is the number of times theprecoding matrix F[i] is used (i=0, 1, 2, . . . , n−1, n), and G_(n,2)is the number of times the precoding matrix F[n] is used.

Condition #124

2×G_(0,2)=G_(1,2)= . . . =G_(i,2)= . . . =G_(n,2), i.e.2×G_(0,2)=G_(a,2) (for ∀a, where a=1, 2, . . . , n−1, n (a being aninteger in a range of 1 to n)).

If the communications system supports a plurality of modulation schemes,and the modulation scheme that is used is selected from among thesupported modulation schemes, then a modulation scheme for whichConditions #119, #120 and #121 (#122, #123 and #124) are satisfiedshould be selected. When a plurality of modulation schemes aresupported, it is typical for the number of bits that can be transmittedin one symbol to vary from modulation scheme to modulation scheme(although it is also possible for the number of bits to be the same),and therefore some modulation schemes may not be capable of satisfyingConditions #119, #120, and #121 (#122, #123 and #124). In such a case,instead of Conditions #119, #120, and #121, the following conditionsshould be satisfied.

Condition #125

The difference between K_(a) and K_(b) is 0 or 1, i.e. |K_(a)−K_(b)| is0 or 1 (for ∀a, ∀b, where a, b, =0, 1, 2, . . . , 2n−1, 2n (each of aand b being an integer in a range of 0 to 2n), and a≠b).

Condition #126

The difference between K_(a,1) and K_(b,1) is 0 or 1, i.e.|K_(a,1)−K_(b,1)| is 0 or 1 (for ∀a, ∀b, where a, b, =0, 1, 2, . . . ,2n−1, 2n (each of a and b being an integer in a range of 0 to 2n), anda≠b).

Condition #127

The difference between K_(a,2) and K_(b,2) is 0 or 1, i.e.|K_(a,2)−K_(b,2)| is 0 or 1 (for ∀a, ∀b, where a, b, =0, 1, 2, . . . ,2n−1, 2n (each of a and b being an integer in a range of 0 to 2n), anda≠b).

Conditions #125, #126 and #127 can also be expressed as follows.

Condition #128

The difference between G_(a) and G_(b) is 0, 1 or 2, i.e. |G_(a)−G_(b)|is 0, 1 or 2 (for ∀a, ∀b, where a, b, =1, 2, . . . , n−1, n (each of aand b being an integer in a range of 1 to n), and a≠b); and

the difference between 2×G₀ and G_(a) is 0, 1 or 2, i.e. |2×G₀−G_(a)|,is 0, 1 or 2 (for ∀a, where a=1, 2, . . . , n−1, n (a being an integerin a range of 1 to n)).

Condition #129

The difference between G_(a,1) and G_(b,1) is 0, 1 or 2, i.e.|G_(a,1)−G_(b,1)| is 0, 1 or 2 (for ∀a, ∀b, where a, b,=1, 2, . . . ,n−1, n (each of a and b being an integer in a range of 1 to n), anda≠b); and

the difference between 2×G_(0,1) and G_(a,1) is 0, 1 or 2, i.e.|2×G_(0,1)−G_(a,1)| is 0, 1 or 2 (for ∀a, where a=1, 2, . . . , n−1, n(a being an integer in a range of 1 to n)).

Condition #130

The difference between G_(a,2) and G_(b,2) is 0, 1 or 2, i.e.|G_(a,2)−G_(b,2)| is 0, 1 or 2 (for ∀a, ∀b, where a, b,=1, 2, . . . ,n−1, n (each of a and b being an integer in a range of 1 to n), anda≠b); and

the difference between 2×G_(0,2) and G_(a,2) is 0, 1 or 2, i.e.|2×G_(0,2)−G_(a,2)| is 0, 1 or 2 (for ∀ a, where a=1, 2, . . . , n−1, n(a being an integer in a range of 1 to n)).

Associating coded blocks with precoding matrices in this way eliminatesbias in the precoding matrices that are used for transmitting codedblocks, thereby achieving the advantageous effect of improving receptionquality of data by the reception device.

In the present embodiment, precoding matrices W[0], W[1], . . . ,W[2n−1], W[2n] (note that W[0], W[1], . . . , W[2n−1], W[2n] arecomposed of F[0], F[1], F[2], . . . , F[n−1], F[n]) for the precodinghopping scheme with the period (cycle) of N=2n+1 slots as described inEmbodiment C2 (the precoding scheme of regularly hopping betweenprecoding matrices with the period (cycle) of N=2n+1 slots) are arrangedin the order W[0], W[1], . . . , W[2n−1], W[2] in the time domain (orthe frequency domain) in the single carrier transmission scheme. Thepresent invention is not, however, limited in this way, and theprecoding matrices W[0], W[1], . . . , W[2n−1], W[2n] may be adapted toa multi-carrier transmission scheme such as an OFDM transmission schemeor the like. As in Embodiment 1, as a scheme of adaption in this case,precoding weights may be changed by arranging symbols in the frequencydomain and in the frequency-time domain. Note that the precoding hoppingscheme with the period (cycle) of N=2n+1 slots has been described, butthe same advantageous effect may be obtained by randomly using theprecoding matrices W[0], W[1], . . . , W[2n−1], W[2n]. In other words,the precoding matrices W[0], W[1], . . . , W[2n−1], W[2n] do not need tobe used in a regular period (cycle). In this case, when the conditionsdescribed in the present embodiment are satisfied, the probability thatthe reception device achieves excellent data reception quality is high.

Furthermore, in the precoding matrix hopping scheme with an H-slotperiod (cycle) (H being a natural number larger than the number of slotsN=2n+1 in the period (cycle) of the above-mentioned scheme of regularlyhopping between precoding matrices), when n+1 different precodingmatrices of the present embodiment are included, the probability ofproviding excellent reception quality increases.

As described in Embodiment 15, there are modes such as the spatialmultiplexing MIMO system, the MIMO system with a fixed precoding matrix,the space-time block coding scheme, the scheme of transmitting onestream and the scheme of regularly hopping between precoding matrices.The transmission device (broadcast station, base station) may select onetransmission scheme from among these modes. In this case, from among thespatial multiplexing MIMO system, the MIMO system with a fixed precodingmatrix, the space-time block coding scheme, the scheme of transmittingone stream and the scheme of regularly hopping between precodingmatrices, a (sub)carrier group selecting the scheme of regularly hoppingbetween precoding matrices may implement the present embodiment.

Embodiment C5

As shown in Non-Patent Literature 12 through Non-Patent Literature 15,the present embodiment describes a case where Embodiment C3 andEmbodiment C4 are generalized when using a Quasi-Cyclic Low-DensityParity-Check (QC-LDPC) code (or an LDPC (block) code other than aQC-LDPC code), a block code such as a concatenated code consisting of anLDPC code and a Bose-Chaudhuri-Hocquenghem (BCH) code, and a block codesuch as a turbo code. The following describes a case of transmitting twostreams s1 and s2 as an example. Note that, when the control informationand the like are not required to perform encoding using the block code,the number of bits constituting the coded block is the same as thenumber of bits constituting the block code (however, the controlinformation and the like described below may be included). When thecontrol information and the like (e.g. CRC (cyclic redundancy check), atransmission parameter) are required to perform encoding using the blockcode, the number of bits constituting the coded block can be a sum ofthe number of bits constituting the block code and the number of bits ofthe control information and the like.

FIG. 97 shows a change in the number of symbols and slots required forone coded block when the block code is used. FIG. 97 shows a change inthe number of symbols and slots required for one coded block when theblock code is used in a case where the two streams s1 and s2 aretransmitted and the transmission device has a single encoder, as shownin the transmission device in FIG. 4 (note that, in this case, eitherthe single carrier transmission or the multi-carrier transmission suchas the OFDM may be used as a transmission system).

As shown in FIG. 97, let the number of bits constituting one coded blockin the block code be 6000 bits. In order to transmit the 6000 bits, 3000symbols, 1500 symbols and 1000 symbols are necessary when the modulationscheme is QPSK, 16QAM and 64QAM, respectively.

Since two streams are to be simultaneously transmitted in thetransmission device shown in FIG. 4, when the modulation scheme is QPSK,1500 symbols are allocated to s1 and remaining 1500 symbols areallocated to s2 out of the above-mentioned 3000 symbols. Therefore, 1500slots (referred to as slots) are necessary to transmit 1500 symbols bys1 and transmit 1500 symbols by s2.

Making the same considerations, 750 slots are necessary to transmit allthe bits constituting one coded block when the modulation scheme is16QAM, and 500 slots are necessary to transmit all the bits constitutingone block when the modulation scheme is 64QAM.

The following describes the relationship between the slots defined aboveand precoding matrices in the scheme of regularly hopping betweenprecoding matrices.

Here, let the precoding matrices for the scheme of regularly hoppingbetween precoding matrices with a five-slot period (cycle) be W[0],W[1], W[2], W[3], W[4]. Note that at least two or more differentprecoding matrices may be included in W[0], W[1], W[2], W[3], W[4] (thesame precoding matrices may be included in W[0], W[1], W[2], W[3],W[4]). In the weighting combination unit of the transmission device inFIG. 4, W[0], W[1], W[2], W[3], W[4] are used (the weighting combinationunit selects one precoding matrix from among a plurality of precodingmatrices in each slot, and performs precoding).

Out of the above-mentioned 1500 slots required to transmit 6000 bits,which is the number of bits constituting one coded block, when themodulation scheme is QPSK, 300 slots are necessary for each of a slotusing the precoding matrix W[0], a slot using the precoding matrix W[1],a slot using the precoding matrix W[2], a slot using the precodingmatrix W[3] and a slot using the precoding matrix W[4]. This is because,if precoding matrices to be used are biased, data reception quality isgreatly influenced by a large number of precoding matrices to be used.

Similarly, out of the above-mentioned 750 slots required to transmit6000 bits, which is the number of bits constituting one coded block,when the modulation scheme is 16QAM, 150 slots are necessary for each ofthe slot using the precoding matrix W[0], the slot using the precodingmatrix W[1], the slot using the precoding matrix W[2], the slot usingthe precoding matrix W[3] and the slot using the precoding matrix W[4].

Similarly, out of the above-mentioned 500 slots required to transmit6000 bits, which is the number of bits constituting one coded block,when the modulation scheme is 64QAM, 100 slots are necessary for each ofthe slot using the precoding matrix W[0], the slot using the precodingmatrix W[1], the slot using the precoding matrix W[2], the slot usingthe precoding matrix W[3] and the slot using the precoding matrix W[4].

As described above, the precoding matrices in the scheme of regularlyhopping between precoding matrices with an N-slot period (cycle) arerepresented as W[0], W[1], W[2], . . . , W[N−2], W[N−1].

Note that W[0], W[1], W[2], . . . , W[N−2], W[N−1] are composed of atleast two or more different precoding matrices (the same precodingmatrices may be included in W[0], W[1], W[2], . . . , W[N−2], W[N−1]).When all the bits constituting one coded block are transmitted, lettingthe number of slots using the precoding matrix W[0] be K₀, letting thenumber of slots using the precoding matrix W[1] be K₁, letting thenumber of slots using the precoding matrix W[i] be K_(i) (i=0, 1, 2, . .. , N−1), and letting the number of slots using the precoding matrixW[N−1] be K_(N-1), the following condition should be satisfied.

Condition #131

K₀=K₁= . . . =K_(i)= . . . =K_(N-1), i.e., K_(a)=K_(b) for ∀a, ∀b (a,b=0,1, 2, . . . , N−1 (a, b are integers from 0 to N−1); a≠b)

When the communication system supports a plurality of modulationschemes, and a modulation scheme is selected and used from among thesupported modulation schemes, Condition #94 should be satisfied.

When the plurality of modulation schemes are supported, however, sincethe number of bits that one symbol can transmit is generally differentdepending on modulation schemes (in some cases, the number of bits canbe the same), there can be a modulation scheme that is not able tosatisfy Condition #131. In such a case, instead of satisfying Condition#131, the following condition may be satisfied.

Condition #132

The difference between K_(a) and K_(b) is 0 or 1, i.e., |K_(a)−K_(b)| is0 or 1 for ∀a, ∀b (a, b=0, 1, 2, . . . , N−1 (a, b are integers from 0to N−1); a≠b)

FIG. 98 shows a change in the number of symbols and slots required fortwo coded blocks when the block code is used. FIG. 98 shows a change inthe number of symbols and slots required for one coded block when theblock code is used in a case where the two streams s1 and s2 aretransmitted and the transmission device has two encoders, as shown inthe transmission device in FIG. 3 and the transmission device in FIG. 13(note that, in this case, either the single carrier transmission or themulti-carrier transmission such as the OFDM may be used as atransmission system).

As shown in FIG. 98, let the number of bits constituting one coded blockin the block code be 6000 bits. In order to transmit the 6000 bits, 3000symbols, 1500 symbols and 1000 symbols are necessary when the modulationscheme is QPSK, 16QAM and 64QAM, respectively.

Since two streams are to be simultaneously transmitted in thetransmission device shown in FIG. 3 and in the transmission device inFIG. 13, and there are two encoders, different coded blocks are to betransmitted. Therefore, when the modulation scheme is QPSK, s1 and s2transmit two coded blocks within the same interval. For example, s1transmits a first coded block, and s2 transmits a second coded block.Therefore, 3000 slots are necessary to transmit the first coded blockand the second coded block.

Making the same considerations, 1500 slots are necessary to transmit allthe bits constituting two coded blocks when the modulation scheme is16QAM, and 1000 slots are necessary to transmit all the bitsconstituting 22 blocks when the modulation scheme is 64QAM.

The following describes the relationship between the slots defined aboveand precoding matrices in the scheme of regularly hopping betweenprecoding matrices.

Here, let the precoding matrices for the scheme of regularly hoppingbetween precoding matrices with a five-slot period (cycle) be W[0],W[1], W[2], W[3], W[4]. Note that at least two or more differentprecoding matrices may be included in W[0], W[1], W[2], W[3], W[4] (thesame precoding matrices may be included in W[0], W[1], W[2], W[3],W[4]). In the weighting combination unit of the transmission device inFIG. 3 and the transmission device in FIG. 13, W[0], W[1], W[2], W[3],W[4] are used (the weighting combination unit selects one precodingmatrix from among a plurality of precoding matrices in each slot, andperforms precoding).

Out of the above-mentioned 3000 slots required to transmit 6000×2 bits,which is the number of bits constituting two coded blocks, when themodulation scheme is QPSK, 600 slots are necessary for each of the slotusing the precoding matrix W[0], the slot using the precoding matrixW[1], the slot using the precoding matrix W[2], the slot using theprecoding matrix W[3] and the slot using the precoding matrix W[4]. Thisis because, if precoding matrices to be used are biased, data receptionquality is greatly influenced by a large number of precoding matrices tobe used.

Also, in order to transmit the first coded block, 600 slots arenecessary for each of the slot using the precoding matrix W[0], the slotusing the precoding matrix W[1], the slot using the precoding matrixW[2], the slot using the precoding matrix W[3] and the slot using theprecoding matrix W[4]. In order to transmit the second coded block, 600slots are necessary for each of the slot using the precoding matrixW[0], the slot using the precoding matrix W[1], the slot using theprecoding matrix W[2], the slot using the precoding matrix W[3] and theslot using the precoding matrix W[4].

Similarly, out of the above-mentioned 1500 slots required to transmit6000×2 bits, which is the number of bits constituting two coded blocks,when the modulation scheme is 64QAM, 300 slots are necessary for each ofthe slot using the precoding matrix W[0], the slot using the precodingmatrix W[1], the slot using the precoding matrix W[2], the slot usingthe precoding matrix W[3] and the slot using the precoding matrix W[4].

Also, in order to transmit the first coded block, 300 slots arenecessary for each of the slot using the precoding matrix W[0], the slotusing the precoding matrix W[1], the slot using the precoding matrixW[2], the slot using the precoding matrix W[3] and the slot using theprecoding matrix W[4]. In order to transmit the second coded block, 300slots are necessary for each of the slot using the precoding matrixW[0], the slot using the precoding matrix W[1], the slot using theprecoding matrix W[2], the slot using the precoding matrix W[3] and theslot using the precoding matrix W[4].

Similarly, out of the above-mentioned 1000 slots required to transmit6000×2 bits, which is the number of bits constituting two coded blocks,when the modulation scheme is 64QAM, 200 slots are necessary for each ofthe slot using the precoding matrix W[0], the slot using the precodingmatrix W[1], the slot using the precoding matrix W[2], the slot usingthe precoding matrix W[3] and the slot using the precoding matrix W[4].

Also, in order to transmit the first coded block, 200 slots arenecessary for each of the slot using the precoding matrix W[0], the slotusing the precoding matrix W[1], the slot using the precoding matrixW[2], the slot using the precoding matrix W[3] and the slot using theprecoding matrix W[4]. In order to transmit the second coded block, 200slots are necessary for each of the slot using the precoding matrixW[0], the slot using the precoding matrix W[1], the slot using theprecoding matrix W[2], the slot using the precoding matrix W[3] and theslot using the precoding matrix W[4].

As described above, the precoding matrices in the scheme of regularlyhopping between precoding matrices with an N-slot period (cycle) arerepresented as W[0], W[1], W[2], . . . , W[N−2], W[N−1].

Note that W[0], W[1], W[2], . . . , W[N−2], W[N−1] are composed of atleast two or more different precoding matrices (the same precodingmatrices may be included in W[0], W[1], W[2], . . . , W[N−2], W[N−1]).When all the bits constituting two coded blocks are transmitted, lettingthe number of slots using the precoding matrix W[0] be K₀, letting thenumber of slots using the precoding matrix W[1] be K₁, letting thenumber of slots using the precoding matrix W[i] be K_(i) (i=0, 1, 2, . .. , N−1), and letting the number of slots using the precoding matrixW[N−1] be K_(N-1), the following condition should be satisfied.

Condition #133

K₀=K₁= . . . =K_(i)= . . . =K_(N-1), i.e., K_(a)=K_(b) for ∀a, ∀b (a,b=0, 1, 2, . . . , N−1 (a, b are integers from 0 to N−1); a≠b)

When all the bits constituting the first coded block are transmitted,letting the number of slots using the precoding matrix W[0] be K_(0,1),letting the number of slots using the precoding matrix W[1] be K_(1,1),letting the number of slots using the precoding matrix W[i] be K_(i,1)(i=0, 1, 2, . . . , N−1), and letting the number of slots using theprecoding matrix W[N−1] be K_(N-1,1), the following condition should besatisfied.

Condition #134

K_(0,1)=K_(1,1)= . . . =K_(i,1)= . . . =K_(N-1,1), i.e., K_(a),1=K_(b,1)for ∀a, ∀b (a, b=0, 1, 2, . . . , N−1 (a, b are integers from 0 to N−1);a≠b)

When all the bits constituting the second coded block are transmitted,letting the number of slots using the precoding matrix W[0] be K_(0,2),letting the number of slots using the precoding matrix W[1] be K_(1,2),letting the number of slots using the precoding matrix W[i] be K_(i,2)(i=0, 1, 2, . . . , N−1), and letting the number of slots using theprecoding matrix W[N−1] be K_(N-1, 2), the following condition should besatisfied.

Condition #135

K_(0,2)=K_(1,2)= . . . =K_(i,2)= . . . =K_(N-1,2), i.e., K_(a,2)=K_(b,2)for ∀a, ∀b (a, b=0, 1, 2, . . . , N−1 (a, b are integers from 0 to N−1);a≠b)

When the communication system supports a plurality of modulationschemes, and a modulation scheme is selected and used from among thesupported modulation schemes, Condition #133, Condition #134 andCondition #135 should be satisfied.

When the plurality of modulation schemes are supported, however, sincethe number of bits that one symbol can transmit is generally differentdepending on modulation schemes (in some cases, the number of bits canbe the same), there can be a modulation scheme that is not able tosatisfy Condition #133, Condition #134 and Condition #135. In such acase, instead of satisfying Condition #133, Condition #134 and Condition#135, the following condition may be satisfied.

Condition #136

The difference between K_(a) and K_(b) is 0 or 1, i.e., |K_(a)−K_(b)| is0 or 1 for ∀a, ∀b (a, b=0, 1, 2, . . . , N−1 (a, b are integers from 0to N−1); a≠b) Condition #137

The difference between K_(a,1) and K_(b,1) is 0 or 1, i.e.,|K_(a,1)−K_(b,1)| is 0 or 1 for ∀a, ∀b (a, b=0, 1, 2, . . . , N−1 (a, bare integers from 0 to N−1); a≠b)

Condition #138

The difference between K_(a,2) and K_(b,2) is 0 or 1, i.e.,K_(a,2)−K_(b,2) is 0 or 1 for ∀a, ∀b (a, b=0, 1, 2, . . . , N−1 (a, bare integers from 0 to N−1); a≠b)

By associating the coded blocks with precoding matrices as describedabove, precoding matrices used to transmit the coded block are unbiased.Therefore, an effect of improving data reception quality in thereception device is obtained.

In the present embodiment, in the scheme of regularly hopping betweenprecoding matrices, N precoding matrices W[0], W[1], W[2], . . . ,W[N−2], W[N−1] are prepared for the precoding hopping scheme with anN-slot period (cycle). There is a way to arrange precoding matrices inthe order W[0], W[1], W[2], . . . , W[N−2], W[N−1] in frequency domain.The present invention is not, however, limited in this way. As describedin Embodiment 1, precoding weights may be changed by arranging Nprecoding matrices W[0], W[1], W[2], . . . , W[N−2], W[N−1] generated inthe present embodiment in time domain and in the frequency-time domain.Note that a precoding hopping scheme with the N-slot period (cycle) hasbeen described, but the same advantageous effect may be obtained byrandomly using N different precoding matrices. In other words, the Ndifferent precoding matrices do not need to be used in a regular period(cycle). In this case, when the conditions described in the presentembodiment are satisfied, the probability that the reception deviceachieves excellent data reception quality is high.

As described in Embodiment 15, there are modes such as the spatialmultiplexing MIMO system, the MIMO system with a fixed precoding matrix,the space-time block coding scheme, the scheme of transmitting onestream and the scheme of regularly hopping between precoding matrices.The transmission device (broadcast station, base station) may select onetransmission scheme from among these modes. In this case, from among thespatial multiplexing MIMO system, the MIMO system with a fixed precodingmatrix, the space-time block coding scheme, the scheme of transmittingone stream and the scheme of regularly hopping between precodingmatrices, a (sub)carrier group selecting the scheme of regularly hoppingbetween precoding matrices may implement the present embodiment.

Supplementary Explanation

In the present description, it is considered that acommunication/broadcasting device such as a broadcast station, a basestation, an access point, a terminal, a mobile phone, or the like isprovided with the transmission device, and that a communication devicesuch as a television, radio, terminal, personal computer, mobile phone,access point, base station, or the like is provided with the receptiondevice. Additionally, it is considered that the transmission device andthe reception device in the present invention have a communicationfunction and are capable of being connected via some sort of interface(such as a USB) to a device for executing applications for a television,radio, personal computer, mobile phone, or the like.

Furthermore, in the present embodiment, symbols other than data symbols,such as pilot symbols (preamble, unique word, postamble, referencesymbol, and the like), symbols for control information, and the like maybe arranged in the frame in any way. While the terms “pilot symbol” and“symbols for control information” have been used here, any term may beused, since the function itself is what is important.

It suffices for a pilot symbol, for example, to be a known symbolmodulated with PSK modulation in the transmission and reception devices(or for the reception device to be able to synchronize in order to knowthe symbol transmitted by the transmission device). The reception deviceuses this symbol for frequency synchronization, time synchronization,channel estimation (estimation of Channel State Information (CSI) foreach modulated signal), detection of signals, and the like.

A symbol for control information is for transmitting information otherthan data (of applications or the like) that needs to be transmitted tothe communication partner for achieving communication (for example, themodulation scheme, error correction coding scheme, coding rate of theerror correction coding scheme, setting information in the upper layer,and the like).

Note that the present invention is not limited to the above Embodiments1-5 and may be embodied with a variety of modifications. For example,the above embodiments describe communication devices, but the presentinvention is not limited to these devices and may be implemented assoftware for the corresponding communication scheme.

Furthermore, a precoding hopping scheme used in a scheme of transmittingtwo modulated signals from two antennas has been described, but thepresent invention is not limited in this way. The present invention maybe also embodied as a precoding hopping scheme for similarly changingprecoding weights (matrices) in the context of a scheme whereby fourmapped signals are precoded to generate four modulated signals that aretransmitted from four antennas, or more generally, whereby N mappedsignals are precoded to generate N modulated signals that aretransmitted from N antennas.

In the present description, the terms “precoding”, “precoding weight”,“precoding matrix” and the like are used, but any term may be used (suchas “codebook”, for example) since the signal processing itself is whatis important in the present invention.

Furthermore, in the present description, the reception device has beendescribed as using ML calculation, APP, Max-log APP, ZF, MMSE, or thelike, which yields soft decision results (log-likelihood, log-likelihoodratio) or hard decision results (“0” or “1”) for each bit of datatransmitted by the transmission device. This process may be referred toas detection, demodulation, estimation, or separation.

Assume that precoded baseband signals z1(i), z2(i) (where i representsthe order in terms of time or frequency (carrier)) are generated byprecoding baseband signals s1(i) and s2(i) for two streams whileregularly hopping between precoding matrices. Let the in-phase componentI and the quadrature component Q of the precoded baseband signal z1(i)be I₁(i) and Q₁(i) respectively, and let the in-phase component I andthe quadrature component Q of the precoded baseband signal z2(i) beI₂(i) and Q₂(i) respectively. In this case, the baseband components maybe switched, and modulated signals corresponding to the switchedbaseband signal r1(i) and the switched baseband signal r2(i) may betransmitted from different antennas at the same time and over the samefrequency by transmitting a modulated signal corresponding to theswitched baseband signal r1(i) from transmit antenna 1 and a modulatedsignal corresponding to the switched baseband signal r2(i) from transmitantenna 2 at the same time and over the same frequency. Basebandcomponents may be switched as follows.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i) and Q₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be I₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i) and I₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₁(i) and Q₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₁(i) and Q₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i) and I₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i) and Q₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₁(i) and I₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be Q₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be I₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be Q₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₁(i) and I₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r₂(i) be I₁(i) and I₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be Q₁(i) and Q₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be Q₁(i) and Q₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₁(i) and I₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr₁(i) be Q₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be Q₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₁(i) and Q₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be I₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₁(i) and Q₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be Q₁(i) and I₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be Q₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be I₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be Q₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be Q₁(i) and I₂(i) respectively. In the above description, signalsin two streams are precoded, and in-phase components and quadraturecomponents of the precoded signals are switched, but the presentinvention is not limited in this way. Signals in more than two streamsmay be precoded, and the in-phase components and quadrature componentsof the precoded signals may be switched.

In the above-mentioned example, switching between baseband signals atthe same time (at the same frequency ((sub)carrier)) has been described,but the present invention is not limited to the switching betweenbaseband signals at the same time. As an example, the followingdescription can be made.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i+v) and Q₂(i+w) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r2(i) be I₂(i+w) and Q₁(i+v) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i+v) and I₂(i+w) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r2(i) be Q₁(i+v) and Q₂(i+w) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₂(i+w) and I₁(i+v) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r2(i) be Q₁(i+v) and Q₂(i+w) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i+v) and I₂(i+w) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r2(i) be Q₂(i+w) and Q₁(i+v) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₂(i+w) and I₁(i+v) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r2(i) be Q₂(i+w) and Q₁(i+v) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i+v) and Q₂(i+w) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r2(i) be Q₁(i+v) and I₂(i+w) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be Q₂(i+w) and I₁(i+v) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r2(i) be I₂(i+w) and Q₁(i+v) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be Q₂(i+w) and I₁(i+v) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r2(i) be Q₁(i+v) and I₂(i+w) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₁(i+v) and I₂(i+w) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r1(i) be Q₁(i+v) and Q₂(i+w) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₂(i+w) and I₁(i+v) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r1(i) be Q₁(i+v) and Q₂(i+w) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₁(i+v) and I₂(i+w) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r1(i) be Q₂(i+w) and Q₁(i+v) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₂(i+w) and I₁(i+v) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r1(i) be Q₂(i+w) and Q₁(i+v) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₁(i+v) and Q₂(i+w) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r1(i) be I₂(i+w) and Q₁(i+v) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₁(i+v) and Q₂(i+w) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r1(i) be Q₁(i+v) and I₂(i+w) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be Q₂(i+w) and I₁(i+v) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r1(i) be I₂(i+w) and Q₁(i+v) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be Q₂(i+w) and I₁(i+v) respectively, and thein-phase component and the quadrature component of the switched basebandsignal r1(i) be Q₁(i+v) and I₂(i+w) respectively.

FIG. 96 explains the above description. As shown in FIG. 96, let thein-phase component I and the quadrature component of the precodedbaseband signal z1(i) be I₁(i) and Q₁(i) respectively, and the in-phasecomponent I and the quadrature component of the precoded baseband signalz2(i) be I₂(i) and Q₂(i) respectively. Then, let the in-phase componentand the quadrature component of the switched baseband signal r1(i) beI_(r1)(i) and Q_(r1)(i) respectively, and the in-phase component and thequadrature component of the switched baseband signal r2(i) be I_(r2)(i)and Q_(r2)(i) respectively, and the in-phase component I_(r1)(i) and thequadrature component Q_(r1)(i) of the switched baseband signal r1(i) andthe in-phase component I_(r2)(i) and the quadrature component Q_(r2)(i)of the switched baseband signal r2(i) are represented by any of theabove descriptions. Note that, in this example, switching betweenprecoded baseband signals at the same time (at the same frequency((sub)carrier)) has been described, but the present invention may beswitching between precoded baseband signals at different times (atdifferent frequencies ((sub)carrier)), as described above.

In this case, modulated signals corresponding to the switched basebandsignal r1(i) and the switched baseband signal r2(i) may be transmittedfrom different antennas at the same time and over the same frequency bytransmitting a modulated signal corresponding to the switched basebandsignal r1(i) from transmit antenna 1 and a modulated signalcorresponding to the switched baseband signal r2(i) from transmitantenna 2 at the same time and over the same frequency.

Each of the transmit antennas of the transmission device and the receiveantennas of the reception device shown in the figures may be formed by aplurality of antennas.

In this description, the symbol “∀” represents the universal quantifier,and the symbol “∃” represents the existential quantifier.

Furthermore, in this description, the units of phase, such as argument,in the complex plane are radians.

When using the complex plane, complex numbers may be shown in polar formby polar coordinates. If a complex number z=a+jb (where a and b are realnumbers and j is an imaginary unit) corresponds to a point (a, b) on thecomplex plane, and this point is represented in polar coordinates as [r,θ], then the following math is satisfied.a=r×cos θb=r×sin θMath 592r=√{square root over (a ² +b ²)}

r is the absolute value of z (r=|z|), and θ is the argument.Furthermore, z=a+jb is represented as re^(jθ).

In the description of the present invention, the baseband signal,modulated signal s1, modulated signal s2, modulated signal z1, andmodulated signal z2 are complex signals. Complex signals are representedas I+jQ (where j is an imaginary unit), I being the in-phase signal, andQ being the quadrature signal. In this case, I may be zero, or Q may bezero.

FIG. 59 shows an example of a broadcasting system that uses the schemeof regularly hopping between precoding matrices described in thisdescription. In FIG. 59, a video encoder 5901 receives video images asinput, encodes the video images, and outputs encoded video images asdata 5902. An audio encoder 5903 receives audio as input, encodes theaudio, and outputs encoded audio as data 5904. A data encoder 5905receives data as input, encodes the data (for example by datacompression), and outputs encoded data as data 5906. Together, theseencoders are referred to as information source encoders 5900.

A transmission unit 5907 receives, as input, the data 5902 of theencoded video, the data 5904 of the encoded audio, and the data 5906 ofthe encoded data, sets some or all of these pieces of data astransmission data, and outputs transmission signals 5908_1 through5908_N after performing processing such as error correction encoding,modulation, and precoding (for example, the signal processing of thetransmission device in FIG. 3). The transmission signals 5908_1 through5908_N are transmitted by antennas 5909_1 through 5909_N as radio waves.

A reception unit 5912 receives, as input, received signals 5911_1through 5911_M received by antennas 5910_1 through 5910_M, performsprocessing such as frequency conversion, decoding of precoding,log-likelihood ratio calculation, and error correction decoding(processing by the reception device in FIG. 7, for example), and outputsreceived data 5913, 5915, and 5917. Information source decoders 5919receive, as input, the received data 5913, 5915, and 5917. A videodecoder 5914 receives, as input, the received data 5913, performs videodecoding, and outputs a video signal. Video images are then shown on atelevision or display monitor. Furthermore, an audio decoder 5916receives, as input, the received data 5915, performs audio decoding, andoutputs an audio signal. Audio is then produced by a speaker. A dataencoder 5918 receives, as input, the received data 5917, performs datadecoding, and outputs information in the data.

In the above embodiments describing the present invention, the number ofencoders in the transmission device when using a multi-carriertransmission scheme such as OFDM may be any number, as described above.Therefore, as in FIG. 4, for example, it is of course possible for thetransmission device to have one encoder and to adapt a scheme ofdistributing output to a multi-carrier transmission scheme such as OFDM.In this case, the wireless units 310A and 310B in FIG. 4 are replaced bythe OFDM related processors 1301A and 1301B in FIG. 13. The descriptionof the OFDM related processors is as per Embodiment 1.

The symbol arrangement scheme described in Embodiments A1 through A5 andin Embodiment 1 may be similarly implemented as a precoding scheme forregularly hopping between precoding matrices using a plurality ofdifferent precoding matrices, the precoding scheme differing from the“scheme for hopping between different precoding matrices” in the presentdescription. The same holds true for other embodiments as well. Thefollowing is a supplementary explanation regarding a plurality ofdifferent precoding matrices.

Let N precoding matrices be represented as F[0], F[1], F[2], . . . ,F[N−3], F[N−2], F[N−1] for a precoding scheme for regularly hoppingbetween precoding matrices. In this case, the “plurality of differentprecoding matrices” referred to above are assumed to satisfy thefollowing two conditions (Condition *1 and Condition *2).

Math 593

Condition *1F[x]≠F[y] for ∀x,∀y(x,y=0,1,2, . . . ,N−3,N−2,N−1;x≠y)

Here, x is an integer from 0 to N−1, y is an integer from 0 to N−1 and xy. With respect to all x and all y satisfying the above, therelationship F[x]≠F[y] holds.

Math 594

Condition *2F[x]=k×F[y]

Letting x be an integer from 0 to N−1, y be an integer from 0 to N−1,and x≠y, for all x and all y, no real or complex number k satisfying theabove equation exists.

The following is a supplementary explanation using a 2×2 matrix as anexample. Let 2×2 matrices R and S be represented as follows:

Math 595

$R = \begin{pmatrix}a & b \\c & d\end{pmatrix}$Math 596

$S = \begin{pmatrix}e & f \\g & h\end{pmatrix}$

Let a=Ae^(jδ11), b=Be^(jδ12), c=Ce^(jδ21) and d=De^(jδ22), ande=Ee^(jγ11), f=Fe^(jγ12), g=Ge^(jγ21) and h=He^(jγ22). A, B, C, D, E, F,G, and H are real numbers 0 or greater, and δ₁₁, δ₁₂, δ₂₁, δ₂₂, γ₁₁,γ₁₂, γ₂₁, and γ₂₂ are expressed in radians. In this case, R≠S means thatat least one of the following holds: (1) a≠e, (2) b≠f, (3) c≠g and (4)d≠h.

A precoding matrix may be the matrix R wherein one of a, b, c, and d iszero. In other words, the precoding matrix may be such that (1) a iszero, and b, c, and d are not zero; (2) b is zero, and a, c, and d arenot zero; (3) c is zero, and a, b, and d are not zero; or (4) d is zero,and a, b, and c are not zero.

In the system example in the description of the present invention, acommunication system using a MIMO scheme was described, wherein twomodulated signals are transmitted from two antennas and are received bytwo antennas. The present invention may, however, of course also beadopted in a communication system using a MISO (Multiple Input SingleOutput) scheme. In the case of the MISO scheme, adoption of a precodingscheme for regularly hopping between a plurality of precoding matricesin the transmission device is the same as described above. On the otherhand, the reception device is not provided with the antenna 701_Y, thewireless unit 703_Y, the channel fluctuation estimating unit 707_1 forthe modulated signal z1, or the channel fluctuation estimating unit707_2 for the modulated signal z2 in the structure shown in FIG. 7. Inthis case as well, however, the processing detailed in the presentdescription may be performed to estimate data transmitted by thetransmission device. Note that it is widely known that a plurality ofsignals transmitted at the same frequency and the same time can bereceived by one antenna and decoded (for one antenna reception, itsuffices to perform calculation such as ML calculation (Max-log APP orthe like)). In the present invention, it suffices for the signalprocessing unit 711 in FIG. 7 to perform demodulation (detection) takinginto consideration the precoding scheme for regularly hopping that isused at the transmitting end.

Programs for executing the above communication scheme may, for example,be stored in advance in ROM (Read Only Memory) and be caused to operateby a CPU (Central Processing Unit).

Furthermore, the programs for executing the above communication schememay be stored in a computer-readable recording medium, the programsstored in the recording medium may be loaded in the RAM (Random AccessMemory) of the computer, and the computer may be caused to operate inaccordance with the programs.

The components in the above embodiments and the like may be typicallyassembled as an LSI (Large Scale Integration), a type of integratedcircuit. Individual components may respectively be made into discretechips, or part or all of the components in each embodiment may be madeinto one chip. While an LSI has been referred to, the terms IC(Integrated Circuit), system LSI, super LSI, or ultra LSI may be useddepending on the degree of integration. Furthermore, the scheme forassembling integrated circuits is not limited to LSI, and a dedicatedcircuit or a general-purpose processor may be used. A FPGA (FieldProgrammable Gate Array), which is programmable after the LSI ismanufactured, or a reconfigurable processor, which allowsreconfiguration of the connections and settings of circuit cells insidethe LSI, may be used.

Furthermore, if technology for forming integrated circuits that replacesLSIs emerges, owing to advances in semiconductor technology or toanother derivative technology, the integration of functional blocks maynaturally be accomplished using such technology. The application ofbiotechnology or the like is possible.

With the symbol arranging scheme described in Embodiments A1 through A5and Embodiment 1, the present invention may be similarly implemented byreplacing the “scheme of hopping between different precoding matrices”with a “scheme of regularly hopping between precoding matrices using aplurality of different precoding matrices”. Note that the “plurality ofdifferent precoding matrices” are as described above.

The above describes that “with the symbol arranging scheme described inEmbodiments A1 through A5 and Embodiment 1, the present invention may besimilarly implemented by replacing the “scheme of hopping betweendifferent precoding matrices” with a “scheme of regularly hoppingbetween precoding matrices using a plurality of different precodingmatrices”. As the “scheme of hopping between precoding matrices using aplurality of different precoding matrices”, a scheme of preparing Ndifferent precoding matrices described above, and hopping betweenprecoding matrices using the N different precoding matrices with anH-slot period (cycle) (H being a natural number larger than N) may beused (as an example, there is a scheme described in Embodiment C2).

With the symbol arranging scheme described in Embodiment 1, the presentinvention may be similarly implemented using the precoding scheme ofregularly hopping between precoding matrices described in Embodiments C1through C5. Similarly, the present invention may be similarlyimplemented using the precoding scheme of regularly hopping betweenprecoding matrices described in Embodiments C1 through C5 as theprecoding scheme of regularly hopping between precoding matricesdescribed in Embodiments A1 through A5.

Embodiment D1

The following describes the scheme of regularly hopping betweenprecoding matrices described in Non-Patent Literatures 12 through 15when using a Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) code (or anLDPC code other than a QC-LDPC code), a concatenated code consisting ofan LDPC code and a Bose-Chaudhuri-Hocquenghem (BCH) code, and a blockcode such as a turbo code or a duo-binary turbo code using tail-biting.Note that the present embodiment may be implemented using either ascheme of regularly hopping between precoding matrices represented bycomplex numbers or a scheme of regularly hopping between precodingmatrices represented by real numbers, which is described below, as thescheme of regularly hopping between precoding matrices.

The following describes a case of transmitting two streams s1 and s2 asan example. Note that, when the control information and the like are notrequired to perform encoding using the block code, the number of bitsconstituting the coded block is the same as the number of bitsconstituting the block code (however, the control information and thelike described below may be included). When the control information andthe like (e.g. CRC (cyclic redundancy check), a transmission parameter)are required to perform encoding using the block code, the number ofbits constituting the coded block can be a sum of the number of bitsconstituting the block code and the number of bits of the controlinformation and the like.

FIG. 97 shows a change in the number of symbols and slots required forone coded block when the block code is used. FIG. 97 shows a change inthe number of symbols and slots required for one coded block when theblock code is used in a case where the two streams s1 and s2 aretransmitted and the transmission device has a single encoder, as shownin the transmission device in FIG. 4 (note that, in this case, eitherthe single carrier transmission or the multi-carrier transmission suchas the OFDM may be used as a transmission system).

As shown in FIG. 97, let the number of bits constituting one coded blockin the block code be 6000 bits. In order to transmit the 6000 bits, 3000symbols, 1500 symbols and 1000 symbols are necessary when the modulationscheme is QPSK, 16QAM and 64QAM, respectively.

Since two streams are to be simultaneously transmitted in thetransmission device shown in FIG. 4, when the modulation scheme is QPSK,1500 symbols are allocated to s1 and remaining 1500 symbols areallocated to s2 out of the above-mentioned 3000 symbols. Therefore, 1500slots (referred to as slots) are necessary to transmit 1500 symbols bys1 and transmit 1500 symbols by s2.

Making the same considerations, 750 slots are necessary to transmit allthe bits constituting one coded block when the modulation scheme is16QAM, and 500 slots are necessary to transmit all the bits constitutingone block when the modulation scheme is 64QAM.

The present embodiment describes a scheme of initializing precodingmatrices in a case where the transmission device in FIG. 4 is compatiblewith the multi-carrier scheme, such as the OFDM scheme, when theprecoding scheme of regularly hopping between precoding matricesdescribed in this description is used.

Next, a case where the transmission device transmits modulated signalseach having a frame structure shown in FIGS. 99A and 99B is considered.FIG. 99A shows a frame structure in the time and frequency domain for amodulated signal z1 (transmitted by the antenna 312A). FIG. 99B shows aframe structure in the time and frequency domain for a modulated signalz2 (transmitted by the antenna 312B). In this case, the modulated signalz1 and the modulated signal z2 are assumed to occupy the same frequency(bandwidth), and the modulated signal z1 and the modulated signal z2 areassumed to exist at the same time.

As shown in FIG. 99A, the transmission device transmits a preamble(control symbol) in an interval A. The preamble is a symbol fortransmitting control information to the communication partner and isassumed to include information on the modulation scheme for transmittingthe first coded block and the second coded block. The transmissiondevice is to transmit the first coded block in an interval B. Thetransmission device is to transmit the second coded block in an intervalC.

The transmission device transmits the preamble (control symbol) in aninterval D. The preamble is a symbol for transmitting controlinformation to the communication partner and is assumed to includeinformation on the modulation scheme for transmitting the third codedblock, the fourth coded block and so on. The transmission device is totransmit the third coded block in an interval E. The transmission deviceis to transmit the fourth coded block in an interval F.

As shown in FIG. 99B, the transmission device transmits a preamble(control symbol) in the interval A. The preamble is a symbol fortransmitting control information to the communication partner and isassumed to include information on the modulation scheme for transmittingthe first coded block and the second coded block. The transmissiondevice is to transmit the first coded block in the interval B. Thetransmission device is to transmit the second coded block in theinterval C.

The transmission device transmits the preamble (control symbol) in theinterval D. The preamble is a symbol for transmitting controlinformation to the communication partner and is assumed to includeinformation on the modulation scheme for transmitting the third codedblock, the fourth coded block and so on. The transmission device is totransmit the third coded block in the interval E. The transmissiondevice is to transmit the fourth coded block in the interval F.

FIG. 100 shows the number of slots used when the coded blocks aretransmitted as shown in FIG. 97, and, in particular, when 16QAM is usedas the modulation scheme in the first coded block. In order to transmitfirst coded block, 750 slots are necessary.

Similarly, FIG. 100 shows the number of slots used when QPSK is used asthe modulation scheme in the second coded block. In order to transmitfirst coded block, 1500 slots are necessary.

FIG. 101 shows the number of slots used when the coded block istransmitted as shown in FIG. 97, and, in particular, when QPSK is usedas the modulation scheme in the third coded block. In order to transmitthird coded block, 1500 slots are necessary.

As described in this description, a case where phase shift is notperformed for the modulated signal z1, i.e. the modulated signaltransmitted by the antenna 312A, and is performed for the modulatedsignal z2, i.e. the modulated signal transmitted by the antenna 312B, isconsidered. In this case, FIGS. 100 and 101 show the scheme of regularlyhopping between precoding matrices.

First, assume that seven precoding matrices are prepared to regularlyhop between the precoding matrices, and are referred to as #0, #1, #2,#3, #4, #5 and #6. The precoding matrices are to be regularly andcyclically used. That is to say, the precoding matrices are to beregularly and cyclically changed in the order #0, #1, #2, #3, #4, #5,#6, #0, #1, #2, #3, #4, #5, #6, #0, #1, #2, #3, #4, #5, #6, . . . .

First, as shown in FIG. 100, 750 slots exist in the first coded block.Therefore, starting from #0, the precoding matrices are arranged in theorder #0, #1, #2, #3, #4, #5, #6, #0, #1, #2, . . . , #4, #5, #6, #0,and end using #0 for the 750^(th) slot.

Next, the precoding matrices are to be applied to each slot in thesecond coded block. Since this description is on the assumption that theprecoding matrices are applied to the multicast communication andbroadcast, one possibility is that a reception terminal does not needthe first coded block and extracts only the second coded block. In sucha case, even when precoding matrix #0 is used to transmit the last slotin the first coded block, the precoding matrix #1 is used first totransmit the second coded block. In this case, the following two schemesare considered:

(a) The above-mentioned terminal monitors how the first coded block istransmitted, i.e. the terminal monitors a pattern of the precodingmatrix used to transmit the last slot in the first coded block, andestimates the precoding matrix to be used to transmit the first slot inthe second coded block; and(b) The transmission device transmits information on the precodingmatrix used to transmit the first slot in the second coded block withoutperforming (a).

In the case of (a), since the terminal has to monitor transmission ofthe first coded block, power consumption increases. In the case of (b),transmission efficiency of data is reduced.

Therefore, there is room for improvement in allocation of precodingmatrices as described above. In order to address the above-mentionedproblems, a scheme of fixing the precoding matrix used to transmit thefirst slot in each coded block is proposed. Therefore, as shown in FIG.100, the precoding matrix used to transmit the first slot in the secondcoded block is set to #0 as with the precoding matrix used to transmitthe first slot in the first coded block.

Similarly, as shown in FIG. 101, the precoding matrix used to transmitthe first slot in the third coded block is set not to #3 but to #0 aswith the precoding matrix used to transmit the first slot in the firstcoded block and in the second coded block.

With the above-mentioned scheme, an effect of suppressing the problemsoccurring in (a) and (b) is obtained.

Note that, in the present embodiment, the scheme of initializing theprecoding matrices in each coded block, i.e. the scheme in which theprecoding matrix used to transmit the first slot in each coded block isfixed to #0, is described. As a different scheme, however, the precodingmatrices may be initialized in units of frames. For example, in thesymbol for transmitting the preamble and information after transmissionof the control symbol, the precoding matrix used in the first slot maybe fixed to #0.

For example, in FIG. 99, a frame is interpreted as starting from thepreamble, the first coded block in the first frame is first coded block,and the first coded block in the second frame is the third coded block.This exemplifies a case where “the precoding matrix used in the firstslot may be fixed (to #0) in units of frames” as described above usingFIGS. 100 and 101.

The following describes a case where the above-mentioned scheme isapplied to a broadcasting system that uses the DVB-T2 standard. Theframe structure of the broadcasting system that uses the DVB-T2 standardis as described in Embodiments A1 through A3. As described inEmbodiments A1 through A3 using FIGS. 61 and 70, by the P1 symbol, P2symbol and control symbol group, information on transmission scheme ofeach PLP (for example, a transmission scheme of transmitting a singlemodulated signal, a transmission scheme using space-time block codingand a transmission scheme of regularly hopping between precodingmatrices) and a modulation scheme being used is transmitted to aterminal. In this case, if the terminal extracts only PLP that isnecessary as information to perform demodulation (including separationof signals and signal detection) and error correction decoding, powerconsumption of the terminal is reduced. Therefore, as described usingFIGS. 99 through 101, the scheme in which the precoding matrix used inthe first slot in the PLP transmitted using, as the transmission scheme,the precoding scheme of regularly hopping between precoding matrices isfixed (to #0) is proposed.

For example, assume that the broadcast station transmits each symbolhaving the frame structure as shown in FIGS. 61 and 70. In this case, asan example, FIG. 102 shows a frame structure in frequency-time domainwhen the broadcast station transmits PLP $1 (to avoid confusion, #1 isreplaced by $1) and PLP $K using the precoding scheme of regularlyhopping between precoding matrices.

Note that, in the following description, as an example, assume thatseven precoding matrices are prepared in the precoding scheme ofregularly hopping between the precoding matrices, and are referred to as#0, #1, #2, #3, #4, #5 and #6. The precoding matrices are to beregularly and cyclically used. That is to say, the precoding matricesare to be regularly and cyclically changed in the order #0, #1, #2, #3,#4, #5, #6, #0, #1, #2, #3, #4, #5, #6, #0, #1, #2, #3, #4, #5, #6, . .. .

As shown in FIG. 102, the slot (symbol) in PLP $1 starts with a time Tand a carrier 3 (10201 in FIG. 102) and ends with a time T+4 and acarrier 4 (10202 in FIG. 102) (see FIG. 102).

This is to say, in PLP $1, the first slot is the time T and the carrier3, the second slot is the time T and the carrier 4, the third slot isthe time T and a carrier 5, . . . , the seventh slot is a time T+1 and acarrier 1, the eighth slot is the time T+1 and a carrier 2, the ninthslot is the time T+1 and the carrier 3, . . . , the fourteenth slot isthe time T+1 and a carrier 8, the fifteenth slot is a time T+2 and acarrier 0,

The slot (symbol) in PLP $K starts with a time S and a carrier 4 (10203in FIG. 102) and ends with a time S+8 and the carrier 4 (10204 in FIG.102) (see FIG. 102).

This is to say, in PLP $K, the first slot is the time S and the carrier4, the second slot is the time S and a carrier 5, the third slot is thetime S and a carrier 6, . . . , the fifth slot is the time S and acarrier 8, the ninth slot is a time S+1 and a carrier 1, the tenth slotis the time S+1 and a carrier 2 . . . , the sixteenth slot is the timeS+1 and the carrier 8, the seventeenth slot is a time S+2 and a carrier0, . . . .

Note that information on slot that includes information on the firstslot (symbol) and the last slot (symbol) in each PLP and is used by eachPLP is transmitted by the control symbol including the P1 symbol, the P2symbol and the control symbol group.

In this case, as described using FIGS. 99 through 101, the first slot inPLP $1, which is the time T and the carrier 3 (10201 in FIG. 102), isprecoded using the precoding matrix #0. Similarly, the first slot in PLP$K, which is the time S and the carrier 4 (10203 in FIG. 102), isprecoded using the precoding matrix #0 regardless of the number of theprecoding matrix used in the last slot in PLP $K−1, which is the time Sand the carrier 3 (10205 in FIG. 102).

The first slot in another PLP transmitted using the precoding scheme ofregularly hopping between the precoding matrices is also precoded usingthe precoding matrix #0.

With the above-mentioned scheme, an effect of suppressing the aboveproblems occurring in (a) and (b) is obtained.

Naturally, the reception device extracts necessary PLP from theinformation on slot that is included in the control symbol including theP1 symbol, the P2 symbol and the control symbol group and is used byeach PLP to perform demodulation (including separation of signals andsignal detection) and error correction decoding. The reception devicelearns a rule of the precoding scheme of regularly hopping between theprecoding matrices in advance (when there are a plurality of rules, thetransmission device transmits information on the rule to be used, andthe reception device learns the rule being used by obtaining thetransmitted information). By synchronizing a timing of rules of hoppingthe precoding matrices based on the number of the first slot in eachPLP, the reception device can perform demodulation of informationsymbols (including separation of signals and signal detection).

Next, a case where the broadcast station (base station) transmits amodulated signal having a frame structure shown in FIG. 103 isconsidered (the frame composed of symbol groups shown in FIG. 103 isreferred to as a main frame). In FIG. 103, elements that operate in asimilar way to FIG. 61 bear the same reference signs. The characteristicfeature is that the main frame is separated into a subframe fortransmitting a single modulated signal and a subframe for transmitting aplurality of modulated signals so that gain control of received signalscan easily be performed. Note that the expression “transmitting a singlemodulated signal” also indicates that a plurality of modulated signalsthat are the same as the single modulated signal transmitted from asingle antenna are generated, and the generated signals are transmittedfrom respective antennas.

In FIG. 103, PLP #1 (6105_1) through PLP #N (6105_N) constitute asubframe 10300 for transmitting a single modulated signal. The subframe10300 is composed only of PLPs, and does not include PLP fortransmitting a plurality of modulated signals. Also, PLP $1 (10302_1)through PLP $M (10302_M) constitute a subframe 10301 for transmitting aplurality of modulated signals. The subframe 10301 is composed only ofPLPs, and does not include PLP for transmitting a single modulatedsignal.

In this case, as described above, when the above-mentioned precodingscheme of regularly hopping between precoding matrices is used in thesubframe 10301, the first slot in PLP (PLP $1 (10302_1) through PLP $M(10302_M)) is assumed to be precoded using the precoding matrix #0(referred to as initialization of the precoding matrices). Theabove-mentioned initialization of precoding matrices, however, isirrelevant to a PLP in which another transmission scheme, for example,one of the transmission scheme using a fixed precoding matrix, thetransmission scheme using a spatial multiplexing MIMO system and thetransmission scheme using the space-time block coding as described inEmbodiments A1 through A3 is used in PLP $1 (10302_1) through PLP $M(10302_M).

As shown in FIG. 104, PLP $1 is assumed to be the first PLP in thesubframe for transmitting a plurality of modulated signals in the X^(th)main frame. Also, PLP $1′ is assumed to be the first PLP in the subframefor transmitting a plurality of modulated signals in the Y^(th) mainframe. Both PLP $1 and PLP $1′ are assumed to use the precoding schemeof regularly hopping between precoding matrices. Note that, in FIG. 104,elements that are similar to the elements shown in FIG. 102 bear thesame reference signs.

In this case, the first slot (10201 in FIG. 104 (time T and carrier 3))in PLP $1, which is the first PLP in the subframe for transmitting aplurality of modulated signals in the X^(th) main frame, is assumed tobe precoded using the precoding matrix #0.

Similarly, the first slot (10401 in FIG. 104 (time T′ and carrier 7)) inPLP $1′, which is the first PLP in the subframe for transmitting aplurality of modulated signals in the Y^(th) main frame, is assumed tobe precoded using the precoding matrix #0.

As described above, in each main frame, the first slot in the first PLPin the subframe for transmitting a plurality of modulated signals ischaracterized by being precoded using the precoding matrix #0.

This is also important to suppress the above-mentioned problemsoccurring in (a) and (b).

Note that, in the present embodiment, as shown in FIG. 97, a case wherethe two streams s1 and s2 are transmitted and the transmission devicehas a single encoder as shown in the transmission device in FIG. 4 istaken as an example. The initialization of precoding matrices describedin the present embodiment, however, is also applicable to a case wherethe two streams s1 and s2 are transmitted and the transmission devicehas two single encoders as shown in the transmission device in FIG. 3,as shown in FIG. 98.

Supplementary Explanation 2

In each of the above-mentioned embodiments, the precoding matrices thatthe weighting combination unit uses for precoding are represented bycomplex numbers. The precoding matrices may also be represented by realnumbers (referred to as a precoding scheme represented by real numbers).

For example, let two mapped baseband signals (in the used modulationscheme) be s1(i) and s2(i) (where i represents time or frequency), andlet two precoded baseband signals obtained by the precoding be z1(i) andz2(i). Then, let the in-phase component and the quadrature component ofthe mapped baseband signal s1(i) (in the used modulation scheme) beI_(s1)(i) and Q_(s1)(i) respectively, the in-phase component and thequadrature component of the mapped baseband signal s2(i) (in the usedmodulation scheme) be I_(s2)(i) and Q_(s2)(i) respectively, the in-phasecomponent and the quadrature component of the precoded baseband signalz1(i) be I_(z1)(i) and Q_(z1)(i) respectively, and in-phase componentand the quadrature component of the precoded baseband signal z2(i) beI_(z2)(i) and Q_(z2)(i) respectively. When the precoding matrix composedof real numbers (the precoding matrix represented by real numbers) H_(r)is used, the following relationship holds.

Math 597

$\begin{pmatrix}{I_{z\; 1}(i)} \\{Q_{z\; 1}(i)} \\{I_{z\; 2}(i)} \\{Q_{z\; 2}(i)}\end{pmatrix} = {H_{r}\begin{pmatrix}{I_{s\; 1}(i)} \\{Q_{s\; 1}(i)} \\{I_{s\; 2}(i)} \\{Q_{s2}(i)}\end{pmatrix}}$

The precoding matrix composed of real numbers H_(r), however, isrepresented as follows.

Math 598

$H_{r} = \begin{pmatrix}a_{11} & a_{12} & a_{13} & a_{14} \\a_{21} & a_{22} & a_{23} & a_{24} \\a_{31} & a_{32} & a_{33} & a_{34} \\a_{41} & a_{42} & a_{43} & a_{44}\end{pmatrix}$

Here, a₁₁, a₁₂, a₁₃, a₁₄, a₂₁, a₂₂, a₂₃, a₂₄, a₃₁, a₃₂, a₃₃, a₃₄, a₄₁,a₄₂, a₄₃ and a₄₄ are real numbers. However, {a₁₁=0, a₁₂=0, a₁₃=0 anda₁₄=0} should not hold, {a₂₁=0, a₂₂=0, a₂₃=0 and a₂₄=0} should not hold,{a₃₁=0, a₃₂=0, a₃₃=0 and a₃₄=0} should not hold and {a₄₁=0, a₄₂=0, a₄₃=0and a₄₄=0} should not hold. Also, {a₁₁=0, a₂₁=0, a₃₁=0 and a₄₁=0} shouldnot hold, {a₁₂=0, a₂₂=0, a₃₂=0 and a₄₂=0} should not hold, {a₁₃=0,a₂₃=0, a₃₃=0 and a₄₃=0} should not hold and {a₁₄=0, a₂₄=0, a₃₄=0 anda₄₄=0} should not hold.

The “scheme of hopping between different precoding matrices” as anapplication of the precoding scheme of the present invention, such asthe symbol arranging scheme described in Embodiments A1 through A5 andEmbodiments 1 and 7, may also naturally be implemented as the precodingscheme of regularly hopping between precoding matrices using theprecoding matrices represented by a plurality of different real numbersdescribed as the “precoding scheme represented by real numbers”. Theusefulness of hopping between precoding matrices in the presentinvention is the same as that in a case where the precoding matrices arerepresented by a plurality of different complex numbers. Note that the“plurality of different precoding matrices” are as described above.

The above describes that “scheme of regularly hopping between differentprecoding matrices” as an application of the precoding scheme of thepresent invention, such as the symbol arranging scheme described inEmbodiments A1 through A5 and Embodiments 1 and 7, may also naturally beimplemented as the precoding scheme of regularly hopping betweenprecoding matrices using the precoding matrices represented by aplurality of different real numbers described as the “precoding schemerepresented by real numbers”. As the “precoding scheme of regularlyhopping between precoding matrices using the precoding matricesrepresented by a plurality of different real numbers”, a scheme ofpreparing N different precoding matrices (represented by real numbers),and hopping between precoding matrices using the N different precodingmatrices (represented by real numbers) with an H-slot period (cycle) (Hbeing a natural number larger than N) may be used (as an example, thereis a scheme described in Embodiment C2).

With the symbol arranging scheme described in Embodiment 1, the presentinvention may be similarly implemented using the precoding scheme ofregularly hopping between precoding matrices described in Embodiments C1through C5. Similarly, the present invention may be similarlyimplemented using the precoding scheme of regularly hopping betweenprecoding matrices described in Embodiments C1 through C5 as theprecoding scheme of regularly hopping between precoding matricesdescribed in Embodiments A1 through A5.

INDUSTRIAL APPLICABILITY

The present invention is widely applicable to wireless systems thattransmit different modulated signals from a plurality of antennas, suchas an OFDM-MIMO system. Furthermore, in a wired communication systemwith a plurality of transmission locations (such as a Power LineCommunication (PLC) system, optical communication system, or DigitalSubscriber Line (DSL) system), the present invention may be adapted toMIMO, in which case a plurality of transmission locations are used totransmit a plurality of modulated signals as described by the presentinvention. A modulated signal may also be transmitted from a pluralityof transmission locations.

REFERENCE SIGNS LIST

-   -   302A, 302B encoder    -   304A, 304B interleaver    -   306A, 306B mapping unit    -   314 weighting information generating unit    -   308A, 308B weighting unit    -   310A, 310B wireless unit    -   312A, 312B antenna    -   402 encoder    -   404 distribution unit    -   504#1,504#2 transmit antenna    -   505#1,505#2 transmit antenna    -   600 weighting unit    -   703_X wireless unit    -   701_X antenna    -   705_1 channel fluctuation estimating unit    -   705_2 channel fluctuation estimating unit    -   707_1 channel fluctuation estimating unit    -   707_2 channel fluctuation estimating unit    -   709 control information decoding unit    -   711 signal processing unit    -   803 INNER MIMO detector    -   805A, 805B log-likelihood calculating unit    -   807A, 807B deinterleaver    -   809A, 809B log-likelihood ratio calculating unit    -   811A, 811B soft-in/soft-out decoder    -   813A, 813B interleaver    -   815 storage unit    -   819 weighting coefficient generating unit    -   901 soft-in/soft-out decoder    -   903 distribution unit    -   1301A, 1301B OFDM related processor    -   1402A, 1402A serial/parallel converter    -   1404A, 1404B reordering unit    -   1406A, 1406B inverse Fast Fourier transformer    -   1408A, 1408B wireless unit    -   2200 precoding weight generating unit    -   2300 reordering unit    -   4002 encoder group

The invention claimed is:
 1. A transmission method for generating aplurality of physical layer pipes (PLPs) and transmitting the pluralityof PLPs from a plurality of antennas in the same frequency at the sametime, the transmission method comprising, in the generation of theplurality of PLPs: generating the plurality of PLPs, the plurality ofPLPs each including a plurality of modulated symbols; selecting onematrix from among N matrices F[i] for each of a plurality of symbols byhopping between the matrices, where i is an integer no less than 0 andno more than N−1, and N is an integer 3 or greater, the N matrices F[i]each defining a precoding process that is performed on a plurality ofbaseband symbols; and generating first precoded signal z1(p) and secondprecoded signal z2(p) by precoding first baseband symbols s1(p) andsecond baseband symbols s2(p) by using the selected one of the Nmatrices F[i], both the first baseband symbols s1(p) and the secondbaseband symbols s2(p) being symbols included in a p-th one of the PLPs,p being an integer 1 or greater and no greater than q, q being aninteger 2 or greater, wherein the first precoded signal z1(p) and thesecond precoded signal z2(p) satisfy:(z1(p),z2(p))^(T) =F[i](s1(p),s2(p))^(T), the N matrices F[i] satisfy:${F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\mspace{11mu}{\theta_{11}{(i)}}} & {\alpha \times {\mathbb{e}}^{j\;{(\;{{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\mspace{11mu}{\theta_{21}{(i)}}}} & {\mathbb{e}}^{j\;{(\;{{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}}$ where λ represents an arbitrary angle, α represents apositive real number, and θ₁₁(i) and θ₂₁(i) satisfy:e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) where xand y are any integers no less than 0 and no more than N−1 and satisfyx≠y, and a same one of the N matrices F[i] is used for a first symbol ofthe first baseband symbols s1(p) and a first symbol of the secondbaseband symbols s2(p).
 2. A transmission apparatus for generating aplurality of physical layer pipes (PLPs) and transmitting the pluralityof PLPs from a plurality of antennas in the same frequency at the sametime, the transmission apparatus comprising: a PLP generating unit thatgenerates the plurality of PLPs, the plurality of PLPs each including aplurality of modulated symbols; a weighting information generating unitthat selects one matrix from among N matrices F[i] for each of aplurality of symbols by hopping between the matrices, where i is aninteger no less than 0 and no more than N−1, and N is an integer 3 orgreater, the N matrices F[i] each defining a precoding process that isperformed on a plurality of baseband symbols; and a weighting unit thatgenerates first precoded signal z1(p) and second precoded signal z2(p)by precoding first baseband symbols s1(p) and second baseband symbolss2(p) by using the selected one of the N matrices F[i], both the firstbaseband symbols s1(p) and the second baseband symbols s2(p) beingsymbols included in a p-th one of the PLPs, p being an integer 1 orgreater and no greater than q, q being an integer 2 or greater, whereinthe first precoded signal z1(p) and the second precoded signal z2(p)satisfy:(z1(p),z2(p))^(T) =F[i](s1(p),s2(p))^(T), the N matrices F[i] satisfy:${F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(i)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}}$ where λ represents an arbitrary angle, α represents apositive real number, and θ₁₁(i) and θ₂₁(i) satisfy:e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) where xand y are any integers no less than 0 and no more than N−1 and satisfyx≠y, and a same one of the N matrices F[i] is used for a first symbol ofthe first baseband symbols s1(p) and a first symbol of the secondbaseband symbols s2(p).
 3. A reception method comprising the step of:receiving a received signal obtained by receiving a plurality ofphysical layer pipes (PLPs) transmitted from a plurality of antennas inthe same frequency at the same time; demodulating the received PLPs byusing a predetermined modulation scheme to obtain a demodulated signal,wherein a p-th one of the PLPs includes first precoded signal z1(p) andsecond precoded signal z2(p), p being an integer 1 or greater and nogreater than q, q being an integer 2 or greater, the first precodedsignal z1(p) and the second precoded signal z2(p) are generated byprecoding first baseband symbols s1(p) and second baseband symbols s2(p)by using a selected matrix, for each of a plurality of symbols, theselected matrix is one matrix selected from among N matrices F[i] byhopping between the matrices, where i is an integer no less than 0 andno more than N−1, and N is an integer 3 or greater, the first precodedsignal z1(p) and the second precoded signal z2(p) satisfy:(z1(p),z ₂(p))^(T) =F[i](s1(p),s2(p))^(T), the N matrices F[i] satisfy:${F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\mspace{11mu}{\theta_{11}{(i)}}} & {\alpha \times {\mathbb{e}}^{j\;{(\;{{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\mspace{11mu}{\theta_{21}{(i)}}}} & {\mathbb{e}}^{j\;{(\;{{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}}$ where λ represents an arbitrary angle, α represents apositive real number, and θ₁₁(i) and θ₂₁(i) satisfy:e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) where xand y are any integers no less than 0 and no more than N−1 and satisfyx≠y, and a same one of the N matrices F[i] is used for a first symbol ofthe first baseband symbols s1(p) and a first symbol of the secondbaseband symbols s2(p).
 4. A reception apparatus comprising: a signalreceiving unit that receives a received signal obtained by receiving aplurality of physical layer pipes (PLPs) transmitted from a plurality ofantennas in the same frequency at the same time; a demodulating unitthat demodulates the received PLPs by using a predetermined modulationscheme to obtain a demodulated signal, wherein a p-th one of the PLPsincludes first precoded signal z1(p) and second precoded signal z2(p), pbeing an integer 1 or greater and no greater than q, q being an integer2 or greater, the first precoded signal z1(p) and the second precodedsignal z2(p) are generated by precoding first baseband symbols s1(p) andsecond baseband symbols s2(p) by using a selected matrix, for each of aplurality of symbols, the selected matrix is one matrix selected fromamong N matrices F[i] by hopping between the matrices, where i is aninteger no less than 0 and no more than N−1, and N is an integer 3 orgreater, the first precoded signal z1(p) and the second precoded signalz2(p) satisfy:(z1(p),z ₂(p))^(T) =F[i](s1(p),s2(p))^(T), the N matrices F[i] satisfy:${F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\mspace{11mu}{\theta_{11}{(i)}}} & {\alpha \times {\mathbb{e}}^{j\;{(\;{{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\mspace{11mu}{\theta_{21}{(i)}}}} & {\mathbb{e}}^{j\;{(\;{{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}}$ where λ represents an arbitrary angle, α represents apositive real number, and θ₁₁(i) and θ₂₁(i) satisfy:e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) where xand y are any integers no less than 0 and no more than N−1 and satisfyx≠y, and a same one of the N matrices F[i] is used for a first symbol ofthe first baseband symbols s1(p) and a first symbol of the secondbaseband symbols s2(p).